Working together, two pumps can drain a certain pool in 4 hours. if it takes the older pump 9 hours to drain the pool by itself, how long will it take the newer pump to drain the pool on its own?

Eight hours because it takes four hours to drain the pool with two new pumps so you multiply 4 x 2 which is 8.

Working together, two pumps can drain a certain pool in 5 hours.
If it takes the older pump 15 hours to drain the pool by itself,
how long will it take the newer pump to drain the pool on its own?
:
you can do this in your head but here is an algebra equation way
:
Let t = time required by new pump to drain the pool
:
Let the completed job (drained pool) = 1
:
 +  = 1
Multiply by 15t
t(5) + 15(5) = 15
5t + 75 = 15t
75 = 15t - 5t
75 = 10t
t = 75/10
t = 7.5 hrs new pump alone
;
:
Check this
5/15 + 5/7.5 =
.33 + .67 = 1