Measurement & Time

Problem

A drifting clock accumulates daily error

A clock runs slow, losing 2 seconds for each hour that passes. It is set correctly at 9:00 a.m. today. I need to find what time it displays three days later when the true time is again 9:00 a.m.
Measurement & dataOperations
Your answer
How to solve
Strategy Identify Subproblems — Break the work into small pieces: first find how many hours pass, then how many seconds are lost, then convert those seconds into minutes and seconds, then subtract from the true time. Tracking units (hours - greater than seconds - greater than minutes) keeps the loss rate honest.
1STEP 1

Count the hours in 3 days

Three full days pass between the two 9:00 a.m. moments. Each day has 24 hours.

3 × 24 = 72 \text{ hours}
2STEP 2

Find the total seconds lost

The clock loses 2 seconds each hour, and 72 hours pass, so multiply the loss rate by the number of hours.

72 × 2 = 144 \text{ seconds}
3STEP 3

Convert 144 seconds to minutes and seconds

Since 60 seconds make 1 minute, regroup 144 seconds: 144 = 120 + 24, and 120 seconds is 2 minutes.

144 \text{ s} = 2 \text{ min } 24 \text{ s}
4STEP 4

Subtract the loss from the true time

A slow clock shows an earlier time, so subtract 2 min 24 s from 9:00:00 a.m. Borrow 1 minute (60 s): 9:00:00 becomes 8:59:60, then subtract.

9{:}00{:}00 - 0{:}02{:}24 = 8{:}57{:}36
Answer
8:57:36 a.m.
9:00:00 − 0:02:24 = 8:57:36
A loss of about 2 minutes 24 seconds over three days is tiny compared to 72 hours, so the clock should read just a few minutes before 9:00 a.m. - and 8:57:36 a.m. is indeed only 2 min 24 s early, which matches.
Takeaway

This only needs Grade 3 multiplication and time-telling: find total seconds lost, then count backward!

  • Count the hours in 3 days
  • Find the total seconds lost
  • Convert 144 seconds to minutes and seconds
  • Subtract the loss from the true time
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