Two pipes are connected to the same tank.

Question

Two pipes are connected to the same tank. When working together, they can fill the tank in 2

hrs. The larger pipe, working alone, can fill the tank in 3

hrs less time than the smaller one. How long would the smaller one take, working alone, to fill the tank?

 

Answer 1

 

 Together, they can fill 1/2 tank per hour.

 

 Let x be the number of hours it takes the smaller pipe to fill the tank.

 It can fill the  1/x of the tank in 1 hour.

 

 The larger pipe can fill the tank in x-3 hours, so it can fill

1/(x-3) of the tank in 1 hour.

 

1/x + 1/(x-3) = 1/2

 

The common denominator is x(x-3)

 

x-3 + x = x(x-3)/2

 

2x - 3 = x(x-3)/2

 

2(2x-3) = x(x-3)

 

4x - 6 = x^2 - 3x

 

0 = x^2 - 3x - 4x + 6

 

0 = x^2 - 7x + 6

 

0 = (  x     -   6)( x   -     1  )

 

x-1 = 0 results in negative times for the larger pipe,

 

 

The smaller pipe fills the tank in 6 hours.

THe larger pipe fills the tank is 3 hours.

 

1/6 + 1/3 = 1/6 + 2/6 = 3/6 = 1/2