KCSE 2025 Maths P1 Q9 — Clock That Loses Time

KCSE 2025 Form 4 Measurement

Published

The Question

“A clock loses 18 seconds every hour. It was set to read the correct time at 8:00 am on Monday. Determine the time, in the 12-hour system, that the clock will read on the following Saturday at 11:20 am.”

1

Find the real time that has passed

First work out how much correct time goes by between when the clock was set and the moment we want to read it. From Monday 8:00 am to Saturday 8:00 am is exactly five full days. From 8:00 am up to 11:20 am is a further 3 hours and 20 minutes. Add these two pieces together to get the total elapsed real time.

5×24=120 hours5 \times 24 = 120 \text{ hours}
120+313=12313 hours=3703 hours120 + 3\tfrac{1}{3} = 123\tfrac{1}{3} \text{ hours} = \frac{370}{3} \text{ hours}

20 minutes is a third of an hour, so 3 hours 20 minutes is 3 and one-third hours.

2

Calculate the total time lost

The clock falls behind by 18 seconds for every hour of real time. Multiply the rate of loss by the number of real hours that have passed. Working with the number of hours as an improper fraction keeps the arithmetic tidy, since the 3 in the denominator cancels neatly into the 18.

Loss=18×3703 seconds\text{Loss} = 18 \times \frac{370}{3} \text{ seconds}
=6×370=2220 seconds= 6 \times 370 = 2220 \text{ seconds}
3

Convert the loss into minutes

The answer is easier to use in minutes, so divide the total seconds by 60. This tells us how far behind the correct time the clock has drifted by Saturday.

222060=37 minutes\frac{2220}{60} = 37 \text{ minutes}
4

Subtract the loss from the real time

Because the clock is losing time it runs slow, so it always shows a time that is behind the true time. To get what it actually reads, take the total loss away from the correct time of 11:20 am. Subtracting 37 minutes from 11:20 gives the clock's reading.

11:20−37 min=10:43 am11{:}20 - 37 \text{ min} = 10{:}43 \text{ am}

Final Result

The clock will read 10:43 am on the following Saturday.

Why this method works

A losing clock accumulates its error steadily, so the total error depends only on how much real time has gone by, not on the clock's own (wrong) reading. That is why we first measure the true elapsed time, multiply by the loss-per-hour rate, and only convert to minutes at the end. Because losing means the hands move too slowly, the displayed time is always earlier than reality, so the accumulated error is subtracted from the correct time rather than added.

✓

37 minutes of loss over 123 and a third hours is about 18 seconds per hour, which matches the given rate, confirming the result.