Reach the next hour, then add the rest

2.MD.C.73.MD.A.1 · take · grade 3

Archetype: Elapsed Time and Base-Sixty Regrouping · step in a 10-type progression

Mia started reading at $1\!:\!50$ p.m. She read a storybook for $35$ minutes, and then read a science book for $47$ minutes.

At what time (p.m.) did Mia finish reading?

Show solution

Understand

Mia started reading at 1:50 p.m. She read a storybook for 35 minutes, then a science book for 47 minutes. Find the time she finished.

Givens

Start time is 1:50 p.m.
First reading lasts 35 minutes.
Second reading lasts 47 minutes.

Unknowns

The clock time (p.m.) when Mia finished reading.

Constraints

Time runs forward; 60 minutes makes one hour.

Plan

#7 Identify Subproblems · also uses: #11 Work Backwards

Rather than adding 35 and 47 across an awkward minute boundary, first add just enough minutes to reach the next whole hour (2:00), then add the rest. This 'make o'clock then add' approach keeps each addition simple.

Execute

#7 Identify Subproblems 2.MD.C.7

From 1:50 it takes 10 minutes to reach 2:00.

60 - 50 = 10 \text{ minutes} \Rightarrow 1{:}50 + 10 = 2{:}00

Topping the minutes up to 60 lands exactly on the next whole hour, which is easy to add onto.

#7 Identify Subproblems 3.MD.A.1

The storybook reading was 35 minutes; 10 of those reached 2:00, so 25 minutes remain.

35 - 10 = 25 \Rightarrow 2{:}00 + 25 = 2{:}25

After hitting the o'clock, adding the leftover minutes is a simple within-the-hour jump.

#7 Identify Subproblems 3.MD.A.1

Now add 47 minutes to 2:25. First reach 3:00 (35 minutes), leaving 12 minutes, so finish at 3:12.

2{:}25 + 35 = 3{:}00,\quad 47 - 35 = 12 \Rightarrow 3{:}00 + 12 = 3{:}12

Using the same make-o'clock trick again keeps the second addition simple.

Answer: 3:12 p.m.

Review

Total reading time is 35 + 47 = 82 minutes = 1 hour 22 minutes. Starting at 1:50, add 1 hour to get 2:50, then 22 minutes to get 3:12 p.m. — matching the step-by-step result.

Add the two durations first: 35 + 47 = 82 minutes = 1 h 22 min, then add to 1:50 p.m. directly to land on 3:12 p.m.

Standards · min grade 3

2.MD.C.7 Tell and write time from analog and digital clocks to nearest five minutes — Reading and stepping the start time up to the next whole hour.
3.MD.A.1 Tell and write time to the nearest minute and solve elapsed time problems — Adding the reading durations across hour boundaries to find the finish time.

💡 Bump up to the next o'clock first, then add what's left: a Grade 3 time-adding shortcut!