If two 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 pipe take to fill the pool on its own?

R1t+t/2.5=1,  we are told it takes both 1.5 hours so

1.5r+0.6=1

1.5r=0.4

r=4/15

So for this other pipe to fill the pool by itself...

4t/15=1

4t=15

t=15/4

t=3.75 hours

check..

4t/15+t/2.5=1

(4t+6t)/15=1

10t=15

t=15/10

t=3/2

t=1.5 hours, correct  (for both pipes filling the pool)