Problema Solution

One pipe can fill a tank 2.5 times faster than another pipe can drain the tank. Starting with an empty tank, if both pipes are turned on, it takes 10 hours to fill the tank. How long does it take the slower pipe working alone to drain a full tank?

Answer provided by our tutors

let


t = hours the first pipe needs to fill a tank alone thus the rate of the first pipe is 1/t tanks per hour

t*2.5 = hours the second pipe needs to drain the tank alone the the rate of the second pipe is 1/(t*2.5) tanks per hour


the rate of the two pipes together is 1/10 tanks per hour


1/t - 1/(t*2.5) = 1/10 multiply both sides by t*2.5


2.5 - 1 = 2.5t/10


2.5t/10 = 1.5


t = 15/2.5


t = 6 hours


t*2.5 = 15 hours


the slower pipe can drain a full tank in 15 hours working alone.