Alliance Form 3 P1 Q12 — Time: A Slow Clock (KCSE Maths)
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The Question
“A clock loses 15 seconds every hour. It is set to the correct time at 7:00 a.m. on Monday. Find the time the clock shows when the correct time is 7:00 p.m. on Wednesday of the same week.”
Find the real time that has passed
Work out the true elapsed time from the moment the clock was set correct until the moment we care about. Go from 7:00 a.m. Monday to 7:00 a.m. Wednesday first — that is two whole days. Then add the extra part of Wednesday, from morning to evening.
Find how much time the clock loses
The clock falls behind by a fixed 15 seconds for each hour of real time. Since 60 real hours have passed, multiply the loss per hour by the number of hours to get the total amount lost.
Convert the loss into minutes
Seconds are hard to read off a clock face, so change the total loss into minutes by dividing by 60 seconds per minute. This tells you how far behind the clock will be reading.
Subtract the loss from the correct time
Because the clock is slow, it lags behind reality — it has not yet reached the true time. So take the correct time and subtract the amount lost. Writing 7:00 p.m. in 24-hour form as 1900 hours makes the subtraction clean.
A slow clock shows an EARLIER time than the real one, so we subtract. A fast clock would show a later time, so you would add.
Final Result
When the correct time is 7:00 p.m. on Wednesday, the slow clock shows 18:45 (that is, 6:45 p.m.).
Why this method works
A clock keeps its own steady but wrong rate, so the error builds up in direct proportion to how long it runs. Losing 15 seconds each hour means the gap between clock and reality grows by the same amount every hour, so total error is simply the hourly loss multiplied by the number of hours. The key idea is direction: 'losing' time means the clock ticks too slowly and therefore reads behind the true time, so the accumulated loss is taken away from the correct time rather than added to it.
Reverse it: 18:45 plus the 15 minutes lost gives 19:00, which is 7:00 p.m. — the correct time, confirming the answer.