Reasoning · Grade 3-1 Length and Time

Problem

Round-Trip Elapsed Time

As planned, the mother reaches the school at 3:00, picks the child up and drives home. The child leaves school at 2:00, walks toward home and is met partway. They arrive 20 minutes early. Find how long the child walked.
Your answer
How to solve
Strategy Draw a Diagram — I draw the road from home to school and mark the meeting point. The 20 minutes saved is exactly the car driving that the mother skipped: she did not drive from the meeting point up to school and back down. Splitting that saved time in half gives the one-way drive time, which tells me when the mother reached the meeting point. Counting from 2:00 to that meeting time gives Mia's walking time.
1STEP 1

See why the trip is 20 minutes shorter

The car skipped the drive up to school and back.

saved time = drive (meeting → school) + drive (school → meeting) = 20 min
2STEP 2

Find the one-way drive time on the skipped stretch

That round trip is 20, so one way is 10 minutes.

20 ÷ 2 = 10 min one way
3STEP 3

Find when the mother reached the meeting point

Due at school at 3:00, she passed the meeting point at 2:50.

3{:}00 - 10 min = 2{:}50 p.m.
4STEP 4

Find how long Mia walked

Walking from 2:00 to 2:50 is 50 minutes.

2{:}50 - 2{:}00 = 50 minutes
Answer
50 minutes
The meeting happened at 2:50, and from there the car would still need 10 minutes to reach school plus the usual drive home; skipping those two 10-minute stretches saves exactly 20 minutes, matching the problem. Walking 50 minutes (2:00 to 2:50) is sensible since Mia left an hour early, so 50 minutes is correct.
Takeaway

The time saved comes from the road the car skipped both ways, so cut it in half to find one trip!

  • See why the trip is 20 minutes shorter
  • Find the one-way drive time on the skipped stretch
  • Find when the mother reached the meeting point
  • Find how long Mia walked