I need alegbra assistance.

Question

I need assistance with the following word problem:

 

A water tank is being filled by two inlet pipes.  Pipe A can fill the tank in 4.5 hours, but both pipes together can fill the tank in 2 hours.  How long does it take to fill the tank using only Pipe B?

Answer 1

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