Question

One pump can drain a pool in 11 minutes. When a second pump is also used, the pool only takes 9 minutes
to drain. How long would it take the second pump to drain the pool if it were the only pump in use?

Answer 1

Let P = the volume of the pool, a be the rate the first pump drains and b be the second.
P/a=11, P/(a+b) = 9
a/P = 1/11, (a+b)/P = 1/9
b/P=1/9-1/11=2/99
P/b=99/2
Therefore, pump b drains the pool in 99/2 minutes. I think

Answer 2

w/a=11
w/(a+b)=9
w/b=?
a=w/11
w/9=a+b, w/9=w/11+b
w/9-w/11=b, 2w/99=b
w/(2w/99)=t(b)
t(b)=99/2=49.5

Answer 3

Moory is correct. However,assuming x be the required answer,it's could be simply be solved like this :

\[ -\frac1{11} - \frac1x = -\frac 19\Rightarrow -\frac1x =-\frac2{99}\Rightarrow x = 49.5\]