How long will it take to fill the pool?

Three water pipes are used to fill a swimming pool. The first pipe alone takes 8 hours to fill the pool, the second pipe alone takes 12 hours to fill the pool, and the third pipe alone takes 24 hours to fill the pool. If all three pipes are opened at the same time, how long will it take to fill the pool?

MetroEye: This problem is similar to work-time problem. Refer MetroEye02

As per the formula,
\(\dfrac{1}{t} = \dfrac{1}{8} + \dfrac{1}{12}+ \dfrac{1}{24}= \dfrac{3 + 2 + 1}{24}  =  \dfrac{6}{24} =  \dfrac{1}{4}\)

=> t = 4

It will take 4 hours to fill the pool if all three pipes are opened at the same time.

Rate of time gain on a "fast" clock

A “fast” clock gains time at the same rate every hour.  It is set to the correct time at 10 a.m. When the fast clock shows 11 a.m. the same day, the correct time is 10:52 a.m. When the fast clock shows 3:30 p.m. that day, what is the correct time?

MetroEye: fast clock gains time at the same rate every hour. 

Number of hours between 10 a.m. and 3.30 p.m. = 5.5 hours
From 10 a.m. to 11 a.m. clock gained 8 minutes => Rate of gain = 8 min/hour

The time gained when the fast clock shows 3.30 p.m. = 5.5 hours * 8 min/hour = 44 mins

The correct time when the fast clock shows 3.30 p.m. = 3.30 p.m. - 44 mins = 2.46 p.m.

So the correct time is 2.46 p.m.