Read a mirrored clock, then find elapsed time

2.MD.C.73.MD.A.1 · take · grade 3

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

Noah took an afternoon nap and then woke up. The pictures below show his clock as seen in a mirror when he fell asleep and when he woke up. For how many hours and minutes did Noah nap?

There are two mirror-image clocks side by side. The left one, labeled "fell asleep," is a clock seen in a mirror (left and right are reversed); once read correctly as a normal clock it shows $4{:}52$ . The right one, labeled "woke up," is also seen in a mirror and read correctly shows $5{:}37$ . Because both clocks are mirror reflections, their left and right sides are swapped.

Show solution

Understand

Two clocks are shown as seen in a mirror. Read correctly, the 'fell asleep' clock is 4:52 and the 'woke up' clock is 5:37. Find how long Noah napped, in hours and minutes.

Givens

The two pictures are mirror images (left and right reversed).
The 'fell asleep' mirrored clock reads as 4:52 once flipped back to normal.
The 'woke up' mirrored clock reads as 5:37 once flipped back to normal.
From the figure, after un-mirroring, the hour hand and minute hand give 4:52 (asleep) and 5:37 (awake).

Unknowns

The nap duration from 4:52 to 5:37 in hours and minutes.

Constraints

Waking time is later than falling-asleep time the same afternoon.

Plan

#17 Visualize Spatial Relationships · also uses: #7 Identify Subproblems

First mentally flip each mirrored clock to read the true time, then find the elapsed time between the two real times by adding a jump to the next o'clock plus the leftover minutes.

Execute

#17 Visualize Spatial Relationships 2.MD.C.7

Flipping the mirror images back to normal reads the true times: fell asleep at 4:52, woke up at 5:37.

\text{asleep } 4{:}52,\ \text{awake } 5{:}37

A mirror swaps left and right, so picturing the flip restores the real clock face.

#7 Identify Subproblems 3.MD.A.1

From 4:52 it takes 8 minutes to reach 5:00.

60 - 52 = 8 \Rightarrow 4{:}52 + 8 = 5{:}00

Stepping up to the whole hour first makes the rest of the count easy.

#7 Identify Subproblems 3.MD.A.1

From 5:00 to 5:37 is another 37 minutes. The total nap is 8 + 37 minutes.

8 + 37 = 45 \text{ minutes}

Both clocks are in the same span under an hour, so the parts add to under one hour.

Answer: 45 minutes (0 hours 45 minutes)

Review

Check by adding: 4:52 + 45 minutes = 5:37, which matches the wake-up time. The nap is under an hour, consistent with the times being only 45 minutes apart.

Subtract directly within the hour reasoning: from 4:52 to 5:37, count minutes 52 to 37 across the hour: 5:37 is 37 minutes past 5, plus the 8 minutes from 4:52 to 5:00, giving 45 minutes.

Standards · min grade 3

2.MD.C.7 Tell and write time from analog and digital clocks to nearest five minutes — Reading the true clock times after un-mirroring the reflected clock faces.
3.MD.A.1 Tell and write time to the nearest minute and solve elapsed time problems — Finding the elapsed nap time between 4:52 and 5:37.

💡 Flip the mirror clock in your head, then count the minutes to the next time: Grade 3 clock-reading plus a spatial flip!