Practice · AM and PM make a 24-hour day · Sensim Math

Variant 1 easy

Noah's family boarded a plane at the airport at 8:20 PM on Sunday and arrived at their destination the next day at 6:10 AM (departure-city time). How many hours and minutes long was Noah's family's flight?

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

A flight left at 8:20 PM Sunday and landed at 6:10 AM the next morning (same departure-city time). We find how long the flight lasted by counting the time from 8:20 PM to midnight, then from midnight to 6:10 AM.

Givens

Departure time: 8:20 PM Sunday
Arrival time: 6:10 AM the next day, in departure-city time
A full day is 24 hours: 12 hours of AM and 12 hours of PM

Unknowns

The flight duration in hours and minutes

Constraints

The flight crosses midnight, so the elapsed time spans from PM into the next AM
Both clock times are in the same time zone, so no zone adjustment is needed

2 · Planchoose the strategy

#7 Identify Subproblems · also uses: #1 Draw a Diagram

Because the flight passes midnight, the cleanest approach splits the elapsed time into two easy pieces: from departure to midnight, and from midnight to arrival. A simple time-line sketch keeps the AM/PM crossing clear, then we add the two pieces.

3 · Execute3 carry out the plan

1Time from departure to midnight

#7 Identify Subproblems 3.MD.A.1

From 8:20 PM to 12:00 midnight is 3 hr 40 min.

12{:}00 - 8{:}20 = 3 \text{ hr } 40 \text{ min}

Midnight ends the PM half of the day, so it is the natural splitting point.

2Time from midnight to arrival

#7 Identify Subproblems 3.MD.A.1

From 12:00 midnight to 6:10 AM is simply 6 hr 10 min, since midnight is the start of the AM half.

6{:}10 - 12{:}00 = 6 \text{ hr } 10 \text{ min}

After midnight the clock reads the AM hours directly, so the second piece is read straight off.

3Add the two pieces

#7 Identify Subproblems 3.MD.A.1

Add the two spans: 3 hr 40 min plus 6 hr 10 min. Minutes: 40 + 10 = 50 min. Hours: 3 + 6 = 9 hr. The total flight time is 9 hr 50 min.

3 \text{ hr } 40 \text{ min} + 6 \text{ hr } 10 \text{ min} = 9 \text{ hr } 50 \text{ min}

Adding the before-midnight and after-midnight pieces gives the whole elapsed time.

Answer: 9 hours 50 minutes

4 · Reviewdoes it hold up?

From about 8 PM to about 6 AM is roughly 9 hours, and our exact answer of 9 hr 50 min fits that estimate. The minutes (50) stayed under 60, so no extra hour was carried, which is consistent.

Another way: Use 24-hour time (tool 15): 8:20 PM is 20:20 and 6:10 AM next day is 30:10; 30:10 - 20:20 = 9 hr 50 min, matching the split-at-midnight method.

Standardsmin grade 3

3.MD.A.1 Tell and write time to the nearest minute and solve elapsed time problems — Finding elapsed time across midnight and adding the two spans

💡Takeaway. When a trip crosses midnight, split the clock at 12:00 into a 'before' and an 'after' piece, then just add them up!

Variant 2 easy

Finn's family boarded a plane at the airport at 9:25 PM on Sunday and arrived at their destination the next day at 1:10 AM (departure-city time). How many hours and minutes long was Finn's family's flight?

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

A flight left at 9:25 PM Sunday and landed at 1:10 AM the next morning (same departure-city time). We find how long the flight lasted by counting the time from 9:25 PM to midnight, then from midnight to 1:10 AM.

Givens

Departure time: 9:25 PM Sunday
Arrival time: 1:10 AM the next day, in departure-city time
A full day is 24 hours: 12 hours of AM and 12 hours of PM

Unknowns

The flight duration in hours and minutes

Constraints

The flight crosses midnight, so the elapsed time spans from PM into the next AM
Both clock times are in the same time zone, so no zone adjustment is needed

2 · Planchoose the strategy

#7 Identify Subproblems · also uses: #1 Draw a Diagram

Because the flight passes midnight, the cleanest approach splits the elapsed time into two easy pieces: from departure to midnight, and from midnight to arrival. A simple time-line sketch keeps the AM/PM crossing clear, then we add the two pieces.

3 · Execute3 carry out the plan

1Time from departure to midnight

#7 Identify Subproblems 3.MD.A.1

From 9:25 PM to 12:00 midnight is 2 hr 35 min.

12{:}00 - 9{:}25 = 2 \text{ hr } 35 \text{ min}

Midnight ends the PM half of the day, so it is the natural splitting point.

2Time from midnight to arrival

#7 Identify Subproblems 3.MD.A.1

From 12:00 midnight to 1:10 AM is simply 1 hr 10 min, since midnight is the start of the AM half.

1{:}10 - 12{:}00 = 1 \text{ hr } 10 \text{ min}

After midnight the clock reads the AM hours directly, so the second piece is read straight off.

3Add the two pieces

#7 Identify Subproblems 3.MD.A.1

Add the two spans: 2 hr 35 min plus 1 hr 10 min. Minutes: 35 + 10 = 45 min. Hours: 2 + 1 = 3 hr. The total flight time is 3 hr 45 min.

2 \text{ hr } 35 \text{ min} + 1 \text{ hr } 10 \text{ min} = 3 \text{ hr } 45 \text{ min}

Adding the before-midnight and after-midnight pieces gives the whole elapsed time.

Answer: 3 hours 45 minutes

4 · Reviewdoes it hold up?

From about 9 PM to about 1 AM is roughly 3 hours, and our exact answer of 3 hr 45 min fits that estimate. The minutes (45) stayed under 60, so no extra hour was carried, which is consistent.

Another way: Use 24-hour time (tool 15): 9:25 PM is 21:25 and 1:10 AM next day is 25:10; 25:10 - 21:25 = 3 hr 45 min, matching the split-at-midnight method.

Standardsmin grade 3

3.MD.A.1 Tell and write time to the nearest minute and solve elapsed time problems — Finding elapsed time across midnight and adding the two spans

💡Takeaway. When a trip crosses midnight, split the clock at 12:00 into a 'before' and an 'after' piece, then just add them up!

Variant 3 easy

Liam's family boarded a plane at the airport at 7:35 PM on Sunday and arrived at their destination the next day at 2:05 AM (departure-city time). How many hours and minutes long was Liam's family's flight?

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

A flight left at 7:35 PM Sunday and landed at 2:05 AM the next morning (same departure-city time). We find how long the flight lasted by counting the time from 7:35 PM to midnight, then from midnight to 2:05 AM.

Givens

Departure time: 7:35 PM Sunday
Arrival time: 2:05 AM the next day, in departure-city time
A full day is 24 hours: 12 hours of AM and 12 hours of PM

Unknowns

The flight duration in hours and minutes

Constraints

The flight crosses midnight, so the elapsed time spans from PM into the next AM
Both clock times are in the same time zone, so no zone adjustment is needed

2 · Planchoose the strategy

#7 Identify Subproblems · also uses: #1 Draw a Diagram

Because the flight passes midnight, the cleanest approach splits the elapsed time into two easy pieces: from departure to midnight, and from midnight to arrival. A simple time-line sketch keeps the AM/PM crossing clear, then we add the two pieces.

3 · Execute3 carry out the plan

1Time from departure to midnight

#7 Identify Subproblems 3.MD.A.1

From 7:35 PM to 12:00 midnight is 4 hr 25 min.

12{:}00 - 7{:}35 = 4 \text{ hr } 25 \text{ min}

Midnight ends the PM half of the day, so it is the natural splitting point.

2Time from midnight to arrival

#7 Identify Subproblems 3.MD.A.1

From 12:00 midnight to 2:05 AM is simply 2 hr 5 min, since midnight is the start of the AM half.

2{:}05 - 12{:}00 = 2 \text{ hr } 5 \text{ min}

After midnight the clock reads the AM hours directly, so the second piece is read straight off.

3Add the two pieces

#7 Identify Subproblems 3.MD.A.1

Add the two spans: 4 hr 25 min plus 2 hr 5 min. Minutes: 25 + 5 = 30 min. Hours: 4 + 2 = 6 hr. The total flight time is 6 hr 30 min.

4 \text{ hr } 25 \text{ min} + 2 \text{ hr } 5 \text{ min} = 6 \text{ hr } 30 \text{ min}

Adding the before-midnight and after-midnight pieces gives the whole elapsed time.

Answer: 6 hours 30 minutes

4 · Reviewdoes it hold up?

From about 7 PM to about 2 AM is roughly 6 hours, and our exact answer of 6 hr 30 min fits that estimate. The minutes (30) stayed under 60, so no extra hour was carried, which is consistent.

Another way: Use 24-hour time (tool 15): 7:35 PM is 19:35 and 2:05 AM next day is 26:05; 26:05 - 19:35 = 6 hr 30 min, matching the split-at-midnight method.

Standardsmin grade 3

3.MD.A.1 Tell and write time to the nearest minute and solve elapsed time problems — Finding elapsed time across midnight and adding the two spans

💡Takeaway. When a trip crosses midnight, split the clock at 12:00 into a 'before' and an 'after' piece, then just add them up!

Variant 4 medium

Olia's family boarded a plane at the airport at 11:40 PM on Sunday and arrived at their destination the next day at 3:25 AM (departure-city time). How many hours and minutes long was Olia's family's flight?

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

A flight left at 11:40 PM Sunday and landed at 3:25 AM the next morning (same departure-city time). We find how long the flight lasted by counting the time from 11:40 PM to midnight, then from midnight to 3:25 AM.

Givens

Departure time: 11:40 PM Sunday
Arrival time: 3:25 AM the next day, in departure-city time
A full day is 24 hours: 12 hours of AM and 12 hours of PM

Unknowns

The flight duration in hours and minutes

Constraints

The flight crosses midnight, so the elapsed time spans from PM into the next AM
Both clock times are in the same time zone, so no zone adjustment is needed

2 · Planchoose the strategy

#7 Identify Subproblems · also uses: #1 Draw a Diagram

Because the flight passes midnight, the cleanest approach splits the elapsed time into two easy pieces: from departure to midnight, and from midnight to arrival. A simple time-line sketch keeps the AM/PM crossing clear, then we add the two pieces.

3 · Execute3 carry out the plan

1Time from departure to midnight

#7 Identify Subproblems 3.MD.A.1

From 11:40 PM to 12:00 midnight is 0 hr 20 min.

12{:}00 - 11{:}40 = 0 \text{ hr } 20 \text{ min}

Midnight ends the PM half of the day, so it is the natural splitting point.

2Time from midnight to arrival

#7 Identify Subproblems 3.MD.A.1

From 12:00 midnight to 3:25 AM is simply 3 hr 25 min, since midnight is the start of the AM half.

3{:}25 - 12{:}00 = 3 \text{ hr } 25 \text{ min}

After midnight the clock reads the AM hours directly, so the second piece is read straight off.

3Add the two pieces

#7 Identify Subproblems 3.MD.A.1

Add the two spans: 0 hr 20 min plus 3 hr 25 min. Minutes: 20 + 25 = 45 min. Hours: 0 + 3 = 3 hr. The total flight time is 3 hr 45 min.

0 \text{ hr } 20 \text{ min} + 3 \text{ hr } 25 \text{ min} = 3 \text{ hr } 45 \text{ min}

Adding the before-midnight and after-midnight pieces gives the whole elapsed time.

Answer: 3 hours 45 minutes

4 · Reviewdoes it hold up?

From about 11 PM to about 3 AM is roughly 3 hours, and our exact answer of 3 hr 45 min fits that estimate. The minutes (45) stayed under 60, so no extra hour was carried, which is consistent.

Another way: Use 24-hour time (tool 15): 11:40 PM is 23:40 and 3:25 AM next day is 27:25; 27:25 - 23:40 = 3 hr 45 min, matching the split-at-midnight method.

Standardsmin grade 3

3.MD.A.1 Tell and write time to the nearest minute and solve elapsed time problems — Finding elapsed time across midnight and adding the two spans

💡Takeaway. When a trip crosses midnight, split the clock at 12:00 into a 'before' and an 'after' piece, then just add them up!

Variant 5 medium

Cora's family boarded a plane at the airport at 11:15 PM on Sunday and arrived at their destination the next day at 4:40 AM (departure-city time). How many hours and minutes long was Cora's family's flight?

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

A flight left at 11:15 PM Sunday and landed at 4:40 AM the next morning (same departure-city time). We find how long the flight lasted by counting the time from 11:15 PM to midnight, then from midnight to 4:40 AM.

Givens

Departure time: 11:15 PM Sunday
Arrival time: 4:40 AM the next day, in departure-city time
A full day is 24 hours: 12 hours of AM and 12 hours of PM

Unknowns

The flight duration in hours and minutes

Constraints

The flight crosses midnight, so the elapsed time spans from PM into the next AM
Both clock times are in the same time zone, so no zone adjustment is needed

2 · Planchoose the strategy

#7 Identify Subproblems · also uses: #1 Draw a Diagram

Because the flight passes midnight, the cleanest approach splits the elapsed time into two easy pieces: from departure to midnight, and from midnight to arrival. A simple time-line sketch keeps the AM/PM crossing clear, then we add the two pieces.

3 · Execute3 carry out the plan

1Time from departure to midnight

#7 Identify Subproblems 3.MD.A.1

From 11:15 PM to 12:00 midnight is 0 hr 45 min.

12{:}00 - 11{:}15 = 0 \text{ hr } 45 \text{ min}

Midnight ends the PM half of the day, so it is the natural splitting point.

2Time from midnight to arrival

#7 Identify Subproblems 3.MD.A.1

From 12:00 midnight to 4:40 AM is simply 4 hr 40 min, since midnight is the start of the AM half.

4{:}40 - 12{:}00 = 4 \text{ hr } 40 \text{ min}

After midnight the clock reads the AM hours directly, so the second piece is read straight off.

3Add the two pieces

#7 Identify Subproblems 3.MD.A.1

Add the two spans: 0 hr 45 min plus 4 hr 40 min. Minutes: 45 + 40 = 85 min (carry 1 hr). Hours: 0 + 4 + 1 = 5 hr. The total flight time is 5 hr 25 min.

0 \text{ hr } 45 \text{ min} + 4 \text{ hr } 40 \text{ min} = 5 \text{ hr } 25 \text{ min}

Adding the before-midnight and after-midnight pieces gives the whole elapsed time.

Answer: 5 hours 25 minutes

4 · Reviewdoes it hold up?

From about 11 PM to about 4 AM is roughly 5 hours, and our exact answer of 5 hr 25 min fits that estimate. The minutes (25) stayed under 60 after one carry, which is consistent.

Another way: Use 24-hour time (tool 15): 11:15 PM is 23:15 and 4:40 AM next day is 28:40; 28:40 - 23:15 = 5 hr 25 min, matching the split-at-midnight method.

Standardsmin grade 3

3.MD.A.1 Tell and write time to the nearest minute and solve elapsed time problems — Finding elapsed time across midnight and adding the two spans

💡Takeaway. When a trip crosses midnight, split the clock at 12:00 into a 'before' and an 'after' piece, then just add them up!

Variant 6 medium

Ezra's family boarded a plane at the airport at 8:45 PM on Sunday and arrived at their destination the next day at 5:05 AM (departure-city time). How many hours and minutes long was Ezra's family's flight?

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

A flight left at 8:45 PM Sunday and landed at 5:05 AM the next morning (same departure-city time). We find how long the flight lasted by counting the time from 8:45 PM to midnight, then from midnight to 5:05 AM.

Givens

Departure time: 8:45 PM Sunday
Arrival time: 5:05 AM the next day, in departure-city time
A full day is 24 hours: 12 hours of AM and 12 hours of PM

Unknowns

The flight duration in hours and minutes

Constraints

The flight crosses midnight, so the elapsed time spans from PM into the next AM
Both clock times are in the same time zone, so no zone adjustment is needed

2 · Planchoose the strategy

#7 Identify Subproblems · also uses: #1 Draw a Diagram

Because the flight passes midnight, the cleanest approach splits the elapsed time into two easy pieces: from departure to midnight, and from midnight to arrival. A simple time-line sketch keeps the AM/PM crossing clear, then we add the two pieces.

3 · Execute3 carry out the plan

1Time from departure to midnight

#7 Identify Subproblems 3.MD.A.1

From 8:45 PM to 12:00 midnight is 3 hr 15 min.

12{:}00 - 8{:}45 = 3 \text{ hr } 15 \text{ min}

Midnight ends the PM half of the day, so it is the natural splitting point.

2Time from midnight to arrival

#7 Identify Subproblems 3.MD.A.1

From 12:00 midnight to 5:05 AM is simply 5 hr 5 min, since midnight is the start of the AM half.

5{:}05 - 12{:}00 = 5 \text{ hr } 5 \text{ min}

After midnight the clock reads the AM hours directly, so the second piece is read straight off.

3Add the two pieces

#7 Identify Subproblems 3.MD.A.1

Add the two spans: 3 hr 15 min plus 5 hr 5 min. Minutes: 15 + 5 = 20 min. Hours: 3 + 5 = 8 hr. The total flight time is 8 hr 20 min.

3 \text{ hr } 15 \text{ min} + 5 \text{ hr } 5 \text{ min} = 8 \text{ hr } 20 \text{ min}

Adding the before-midnight and after-midnight pieces gives the whole elapsed time.

Answer: 8 hours 20 minutes

4 · Reviewdoes it hold up?

From about 8 PM to about 5 AM is roughly 8 hours, and our exact answer of 8 hr 20 min fits that estimate. The minutes (20) stayed under 60, so no extra hour was carried, which is consistent.

Another way: Use 24-hour time (tool 15): 8:45 PM is 20:45 and 5:05 AM next day is 29:05; 29:05 - 20:45 = 8 hr 20 min, matching the split-at-midnight method.

Standardsmin grade 3

3.MD.A.1 Tell and write time to the nearest minute and solve elapsed time problems — Finding elapsed time across midnight and adding the two spans

💡Takeaway. When a trip crosses midnight, split the clock at 12:00 into a 'before' and an 'after' piece, then just add them up!

Variant 7 medium

Emma's family boarded a plane at the airport at 10:30 PM on Sunday and arrived at their destination the next day at 5:45 AM (departure-city time). How many hours and minutes long was Emma's family's flight?

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

A flight left at 10:30 PM Sunday and landed at 5:45 AM the next morning (same departure-city time). We find how long the flight lasted by counting the time from 10:30 PM to midnight, then from midnight to 5:45 AM.

Givens

Departure time: 10:30 PM Sunday
Arrival time: 5:45 AM the next day, in departure-city time
A full day is 24 hours: 12 hours of AM and 12 hours of PM

Unknowns

The flight duration in hours and minutes

Constraints

The flight crosses midnight, so the elapsed time spans from PM into the next AM
Both clock times are in the same time zone, so no zone adjustment is needed

2 · Planchoose the strategy

#7 Identify Subproblems · also uses: #1 Draw a Diagram

Because the flight passes midnight, the cleanest approach splits the elapsed time into two easy pieces: from departure to midnight, and from midnight to arrival. A simple time-line sketch keeps the AM/PM crossing clear, then we add the two pieces.

3 · Execute3 carry out the plan

1Time from departure to midnight

#7 Identify Subproblems 3.MD.A.1

From 10:30 PM to 12:00 midnight is 1 hr 30 min.

12{:}00 - 10{:}30 = 1 \text{ hr } 30 \text{ min}

Midnight ends the PM half of the day, so it is the natural splitting point.

2Time from midnight to arrival

#7 Identify Subproblems 3.MD.A.1

From 12:00 midnight to 5:45 AM is simply 5 hr 45 min, since midnight is the start of the AM half.

5{:}45 - 12{:}00 = 5 \text{ hr } 45 \text{ min}

After midnight the clock reads the AM hours directly, so the second piece is read straight off.

3Add the two pieces

#7 Identify Subproblems 3.MD.A.1

Add the two spans: 1 hr 30 min plus 5 hr 45 min. Minutes: 30 + 45 = 75 min (carry 1 hr). Hours: 1 + 5 + 1 = 7 hr. The total flight time is 7 hr 15 min.

1 \text{ hr } 30 \text{ min} + 5 \text{ hr } 45 \text{ min} = 7 \text{ hr } 15 \text{ min}

Adding the before-midnight and after-midnight pieces gives the whole elapsed time.

Answer: 7 hours 15 minutes

4 · Reviewdoes it hold up?

From about 10 PM to about 5 AM is roughly 7 hours, and our exact answer of 7 hr 15 min fits that estimate. The minutes (15) stayed under 60 after one carry, which is consistent.

Another way: Use 24-hour time (tool 15): 10:30 PM is 22:30 and 5:45 AM next day is 29:45; 29:45 - 22:30 = 7 hr 15 min, matching the split-at-midnight method.

Standardsmin grade 3

3.MD.A.1 Tell and write time to the nearest minute and solve elapsed time problems — Finding elapsed time across midnight and adding the two spans

💡Takeaway. When a trip crosses midnight, split the clock at 12:00 into a 'before' and an 'after' piece, then just add them up!

Variant 8 hard

Mila's family boarded a plane at the airport at 10:50 PM on Sunday and arrived at their destination the next day at 6:35 AM (departure-city time). How many hours and minutes long was Mila's family's flight?

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

A flight left at 10:50 PM Sunday and landed at 6:35 AM the next morning (same departure-city time). We find how long the flight lasted by counting the time from 10:50 PM to midnight, then from midnight to 6:35 AM.

Givens

Departure time: 10:50 PM Sunday
Arrival time: 6:35 AM the next day, in departure-city time
A full day is 24 hours: 12 hours of AM and 12 hours of PM

Unknowns

The flight duration in hours and minutes

Constraints

The flight crosses midnight, so the elapsed time spans from PM into the next AM
Both clock times are in the same time zone, so no zone adjustment is needed

2 · Planchoose the strategy

#7 Identify Subproblems · also uses: #1 Draw a Diagram

Because the flight passes midnight, the cleanest approach splits the elapsed time into two easy pieces: from departure to midnight, and from midnight to arrival. A simple time-line sketch keeps the AM/PM crossing clear, then we add the two pieces.

3 · Execute3 carry out the plan

1Time from departure to midnight

#7 Identify Subproblems 3.MD.A.1

From 10:50 PM to 12:00 midnight is 1 hr 10 min.

12{:}00 - 10{:}50 = 1 \text{ hr } 10 \text{ min}

Midnight ends the PM half of the day, so it is the natural splitting point.

2Time from midnight to arrival

#7 Identify Subproblems 3.MD.A.1

From 12:00 midnight to 6:35 AM is simply 6 hr 35 min, since midnight is the start of the AM half.

6{:}35 - 12{:}00 = 6 \text{ hr } 35 \text{ min}

After midnight the clock reads the AM hours directly, so the second piece is read straight off.

3Add the two pieces

#7 Identify Subproblems 3.MD.A.1

Add the two spans: 1 hr 10 min plus 6 hr 35 min. Minutes: 10 + 35 = 45 min. Hours: 1 + 6 = 7 hr. The total flight time is 7 hr 45 min.

1 \text{ hr } 10 \text{ min} + 6 \text{ hr } 35 \text{ min} = 7 \text{ hr } 45 \text{ min}

Adding the before-midnight and after-midnight pieces gives the whole elapsed time.

Answer: 7 hours 45 minutes

4 · Reviewdoes it hold up?

From about 10 PM to about 6 AM is roughly 7 hours, and our exact answer of 7 hr 45 min fits that estimate. The minutes (45) stayed under 60, so no extra hour was carried, which is consistent.

Another way: Use 24-hour time (tool 15): 10:50 PM is 22:50 and 6:35 AM next day is 30:35; 30:35 - 22:50 = 7 hr 45 min, matching the split-at-midnight method.

Standardsmin grade 3

3.MD.A.1 Tell and write time to the nearest minute and solve elapsed time problems — Finding elapsed time across midnight and adding the two spans

💡Takeaway. When a trip crosses midnight, split the clock at 12:00 into a 'before' and an 'after' piece, then just add them up!

Variant 9 hard

Aria's family boarded a plane at the airport at 9:05 PM on Sunday and arrived at their destination the next day at 7:50 AM (departure-city time). How many hours and minutes long was Aria's family's flight?

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

A flight left at 9:05 PM Sunday and landed at 7:50 AM the next morning (same departure-city time). We find how long the flight lasted by counting the time from 9:05 PM to midnight, then from midnight to 7:50 AM.

Givens

Departure time: 9:05 PM Sunday
Arrival time: 7:50 AM the next day, in departure-city time
A full day is 24 hours: 12 hours of AM and 12 hours of PM

Unknowns

The flight duration in hours and minutes

Constraints

The flight crosses midnight, so the elapsed time spans from PM into the next AM
Both clock times are in the same time zone, so no zone adjustment is needed

2 · Planchoose the strategy

#7 Identify Subproblems · also uses: #1 Draw a Diagram

Because the flight passes midnight, the cleanest approach splits the elapsed time into two easy pieces: from departure to midnight, and from midnight to arrival. A simple time-line sketch keeps the AM/PM crossing clear, then we add the two pieces.

3 · Execute3 carry out the plan

1Time from departure to midnight

#7 Identify Subproblems 3.MD.A.1

From 9:05 PM to 12:00 midnight is 2 hr 55 min.

12{:}00 - 9{:}05 = 2 \text{ hr } 55 \text{ min}

Midnight ends the PM half of the day, so it is the natural splitting point.

2Time from midnight to arrival

#7 Identify Subproblems 3.MD.A.1

From 12:00 midnight to 7:50 AM is simply 7 hr 50 min, since midnight is the start of the AM half.

7{:}50 - 12{:}00 = 7 \text{ hr } 50 \text{ min}

After midnight the clock reads the AM hours directly, so the second piece is read straight off.

3Add the two pieces

#7 Identify Subproblems 3.MD.A.1

Add the two spans: 2 hr 55 min plus 7 hr 50 min. Minutes: 55 + 50 = 105 min (carry 1 hr). Hours: 2 + 7 + 1 = 10 hr. The total flight time is 10 hr 45 min.

2 \text{ hr } 55 \text{ min} + 7 \text{ hr } 50 \text{ min} = 10 \text{ hr } 45 \text{ min}

Adding the before-midnight and after-midnight pieces gives the whole elapsed time.

Answer: 10 hours 45 minutes

4 · Reviewdoes it hold up?

From about 9 PM to about 7 AM is roughly 10 hours, and our exact answer of 10 hr 45 min fits that estimate. The minutes (45) stayed under 60 after one carry, which is consistent.

Another way: Use 24-hour time (tool 15): 9:05 PM is 21:05 and 7:50 AM next day is 31:50; 31:50 - 21:05 = 10 hr 45 min, matching the split-at-midnight method.

Standardsmin grade 3

3.MD.A.1 Tell and write time to the nearest minute and solve elapsed time problems — Finding elapsed time across midnight and adding the two spans

💡Takeaway. When a trip crosses midnight, split the clock at 12:00 into a 'before' and an 'after' piece, then just add them up!

Variant 10 hard

Liam's family boarded a plane at the airport at 9:55 PM on Sunday and arrived at their destination the next day at 4:15 AM (departure-city time). How many hours and minutes long was Liam's family's flight?

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

A flight left at 9:55 PM Sunday and landed at 4:15 AM the next morning (same departure-city time). We find how long the flight lasted by counting the time from 9:55 PM to midnight, then from midnight to 4:15 AM.

Givens

Departure time: 9:55 PM Sunday
Arrival time: 4:15 AM the next day, in departure-city time
A full day is 24 hours: 12 hours of AM and 12 hours of PM

Unknowns

The flight duration in hours and minutes

Constraints

The flight crosses midnight, so the elapsed time spans from PM into the next AM
Both clock times are in the same time zone, so no zone adjustment is needed

2 · Planchoose the strategy

#7 Identify Subproblems · also uses: #1 Draw a Diagram

Because the flight passes midnight, the cleanest approach splits the elapsed time into two easy pieces: from departure to midnight, and from midnight to arrival. A simple time-line sketch keeps the AM/PM crossing clear, then we add the two pieces.

3 · Execute3 carry out the plan

1Time from departure to midnight

#7 Identify Subproblems 3.MD.A.1

From 9:55 PM to 12:00 midnight is 2 hr 5 min.

12{:}00 - 9{:}55 = 2 \text{ hr } 5 \text{ min}

Midnight ends the PM half of the day, so it is the natural splitting point.

2Time from midnight to arrival

#7 Identify Subproblems 3.MD.A.1

From 12:00 midnight to 4:15 AM is simply 4 hr 15 min, since midnight is the start of the AM half.

4{:}15 - 12{:}00 = 4 \text{ hr } 15 \text{ min}

After midnight the clock reads the AM hours directly, so the second piece is read straight off.

3Add the two pieces

#7 Identify Subproblems 3.MD.A.1

Add the two spans: 2 hr 5 min plus 4 hr 15 min. Minutes: 5 + 15 = 20 min. Hours: 2 + 4 = 6 hr. The total flight time is 6 hr 20 min.

2 \text{ hr } 5 \text{ min} + 4 \text{ hr } 15 \text{ min} = 6 \text{ hr } 20 \text{ min}

Adding the before-midnight and after-midnight pieces gives the whole elapsed time.

Answer: 6 hours 20 minutes

4 · Reviewdoes it hold up?

From about 9 PM to about 4 AM is roughly 6 hours, and our exact answer of 6 hr 20 min fits that estimate. The minutes (20) stayed under 60, so no extra hour was carried, which is consistent.

Another way: Use 24-hour time (tool 15): 9:55 PM is 21:55 and 4:15 AM next day is 28:15; 28:15 - 21:55 = 6 hr 20 min, matching the split-at-midnight method.

Standardsmin grade 3

3.MD.A.1 Tell and write time to the nearest minute and solve elapsed time problems — Finding elapsed time across midnight and adding the two spans

💡Takeaway. When a trip crosses midnight, split the clock at 12:00 into a 'before' and an 'after' piece, then just add them up!

AM and PM make a 24-hour day · 10 practice problems

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