Question

Pump A can fill a tank of water in 5 hours. Pump B can fill the same tank in 8 hours. How long does it take the two pumps working together to fill the tank?(round your answer to the nearest minute).

Answer 1

185 min

Explanation:

Data

Pump a = Pa

Pump b = Pb

Full Tank = Ft

Tank = T

we have that Pa fills T in 5 hours and Pb fills the same tank in 8 hours, we must find that T capacity is filled in one hour by Pa and Pb

if Pa fills T in 5h, in 1h what capacity is filled,
`Pa=(h*Ft)/(5h)=(Ft)/(5)` ; if Pb fills T in 8h, in 1h what capacity is filled,
`Pb=(h*Ft)/(8h)=(Ft)/(8)`, and now we must find:

How long will Pa and Pa be used together to fill T

.
`Pa+Pb = (Ft)/(5)+(Ft)/(8)=(13Ft)/(40)`; The capacity of T = 40/40, so if Pa+Pa in 1h fill
`(13Ft)/(40)` then to fill 40/40 in h=?

`(1h*(40)/(40)Ft )/((13Ft)/(40))=((40Ft.h)/(40))/((13Ft)/(40))=(40h)/(13)`, but h must be in min so

`(40h)/(13)*(60min)/(h)=185 min`