lets

t hours by the time needed when the 2 pumps are working together thus their rate is 1 pool in t hours or

1/t pools per hour

o hours the time the older pump needs to drain the pool by itself thus its rate is 1 pool in o hours or

1/o pools per hour

n = ? the time the newer pump needs to drain the pool by itself has a rate 1 pool in n hours or

1/n pools per hour

now we can write

1/o + 1/n = 1/t

1/n = 1/t - 1/o

n = 1/(1/t - 1/o)

n = (t*o)/(o - t) hours

new newer pump will need (t*o)/(o - t) hours to drain the pool on its own.