How do i do this problem

Question

If 2 inlet pipes can fill a pool in one hour and 30 minutes, and one pipe can fill the pool in two hours and 30 minutes on its own, how long would the other pope take to fill the pool on its own?

Answer 1

one pipe fills the pool in 2 1/2 hours

a second pipe fills the pool in x hours (this is what we are trying to find out)

pipe one fills 1/(2 1/2) of the pool in 1 hour

pipe two fills 1/x of the pool in one hour

together it takes both pipes 1 1/2 hours

(1/2 1/2)=1/(5/2)=2/5

(2/5)(1 1/2)+(1/x)( 1 1/2)=1 (job finished)

1 1/2=3/2

(2/5)(3/2)+(1/x)(3/2)=1

(6/10)+(3/2x)=1

(3/5)+(3/2x)=1

multiply both sides by 10x

10x(3/5)+10x(3/2x)=10x(1)

(30x/5)+30x/2x)=10x

6x+15=10x

10x-6x=15

4x=15

x=15/4

x=3 3/4 hours  for the other pipe to fill the pool alone

check:(1/3.75)(1.5)+(1/2.5)(1.5)=1

(1.5/3.75)+(1.5/2.5)=1

0.4+0.6=1

1=1