Edward C. answered • 04/20/15

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Let T = time for Pipe B to fill tank

Pipe A can fill in 4.5 hours ==> in 1 hour Pipe A can fill 1/4.5 of the tank

Pipe B can fill in T hours ==> in 1 hour Pipe B can fill 1/T of the tank

Both Pipes can fill in 2 hours ==> in 1 hour both Pipes fill 1/2 of the tank

In 1 hour, the sum of the amounts of the tank that Pipe A and Pipe B can fill separately

(which is 1/4.5 + 1/T)

must equal the amount that they can fill together (which is 1/2) so

1/4.5 + 1/T = 1/2

Multiply both sides by 18*T to clear fractions

4*T + 18 = 9*T

5*T = 18

T = 18/5 = 3.6 hours to fill the tank using only Pipe B