Math Slow Clock Problem?

Question

A clock loses 15 minutes each hour. If the clock is set correctly at 12 o clock noon, what is the correct time when the clock reads 4pm?

I have been trying to figure this riddle out for a while now, I just cant get it... what formula/steps do you use to figure it out?

Answer 1

If the clock loses 15 minutes every hour it only moves 3/4 of an hour every hour.

Let

x = acual amount of time passed

(3/4)x = 4
x = 4(4/3) = 16/3 hours.

So the actual time is 5 1/3 hours = 5:20 pm
when the slow clock shows 4:00 pm.

Answer 2

Remember that every hour the clock would only go ahead 45 minutes instead of an hour.

Then you get to the clock saying 3:45 and the real time being 5:00. I think this is where you get stuck.

From 3:45 to 4:00 is 15 minutes, so you want to know how much the clock loses in 15 minutes. Make a proportion:

15 / 60 = x / 15
60x =225
x = 3.75

So every 15 minutes, the clock loses 3.75 minutes.

That leaves the clock saying 3:56 (and 25 seconds) when it is 5:15.

So make a proportion again.

15 / 60 = x / 4
60x = 60
x = 1
(In 4 minutes, the clock goes ahead 3)

The clock now says 3:59 (and 25 seconds) when it is 5:19.

15 / 60 = x / 1
60x = 15
x = 1/4
(In 1 minute, the clock goes ahead 3/4 a minute)

The clock now says 4:00 exactly! and the real time is 5:20.

There probably was an easier way to do that, but that's the answer. 5:20.

Hope that helps and thanks for the riddle!

Answer 3

Math Problem Clock