Operations & Word Problems

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Find the daily gap between a clock and true time

A clock runs fast by a steady 5145\frac{1}{4} minutes every 33 days. It was set exactly right at 22 p.m. one day. What time will it show at 22 p.m. the next day, in hours, minutes and seconds?

Number systemRatios
Your answer
How to solve
Strategy Identify Subproblems — The gain is given over three days but asked about over one, so find the one-day amount first. It comes out as a fraction of a minute, which then has to be read back as seconds before it can be written as a clock time.
1STEP 1

Find one day's gain

The clock gains 5 1/4 minutes over 3 days at a steady rate, so divide by 3 to get a single day's gain.

21/4 ÷ 3 = 7/4
2STEP 2

Turn the fraction of a minute into seconds

7/4 minutes is 1 whole minute and 3/4 of another. Three quarters of 60 seconds is 45 seconds.

3/4 × 60 = 45
3STEP 3

Add the gain to the true time

A clock that runs fast shows a time later than the true one, so add the gain to 2 p.m.

2:00:00 + 0:01:45 = 2:01:45
Answer
2:01:45 p.m.
Check by tripling: three days of 1 minute 45 seconds is 5 minutes 15 seconds, and 5 1/4 minutes is exactly 5 minutes 15 seconds.
Takeaway

When a rate is given over several days but asked about one, find the one-day amount first.

  • Find one day's gain
  • Turn the fraction of a minute into seconds
  • Add the gain to the true time
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