Question

Lesson 5.3: Rational

2.
Jill is filling a water trough for her horse. Using pump A, the trough is filled up in half an
hour. Using pump B, the trough is filled up in three quarters of an hour. How long does it
take to fill the trough using both pumps?

Answer 1

It will take 18 minutes to fill the trough using both pumps.

Explanation:

Given that:

Time taken by pump A = half hour = 30 minutes

Time taken by pump B = three quarters of an hour

One quarter =
`(1)/(4)`

One hour = 60 minutes

Three quarters of an hour =
`(3)/(4)*60` = 45 minutes

Let,

x be the time taken by both pumps to fill the trough.

`(1)/(time\ taken\ by\ pump\ A)+(1)/(time\ taken\ by\ pump\ B)=(1)/(Time\ taken\ by\ both\ pumps)`

`(1)/(30)+(1)/(45)=(1)/(x)\\\\(3+2)/(90)=(1)/(x)\\\\(5)/(90)=(1)/(x)\\\\(1)/(18)=(1)/(x)\\x=18`

Hence,

It will take 18 minutes to fill the trough using both pumps.