Question

College Algebra

A winery has a vat with two pipes leading to it. The inlet pipe can fill the vat in 5 hours, while the outlet pipe can empty it in 8 hours. How long will it take to fill the vat if both pipes are left open?

It will take__ hours.
(Simplify your answer. Do not round.)

Answer 1

3 1/13

Explanation:

rate(time) of one pipe + rate(time) of the other pipe = 1 job

The rate would be the the number of jobs over the time

The rate of the first pipe is 1/5 and the rate of the second pipe is 1/8.

Together:

1/5t + 1/8t = I job

t(1/5 + 1/8) = 1

t(8/40 + 5/40) = 1

t(13/40) = 1 multiply each side by 40/13

t(40/13)(13/40) = 1(40/13)

t = 40/13

t = 3 1/13