SOLUTION: Two pipes can fill a tank in two hours it the first tank three hours longer than the second tank. How long would it take each pipe alone? thank you

Hi,

Let x represent the time second tank would take alone.  

then the time the first tank to fill alone would be(x+3)

***Two pipes can fill a tank in two hours.  Per hour is the equalizer.

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

Mulitplying each term on both sides of the equation by 2x(x+3) so as all denominaotrs = 1

2(x+3) + 2x = x(x+3)

solving for x

2x + 6 + 2x = x^2 + 3x

x^2 -x -6 = 0

factoring

(x-3)(x+1)= 0

(x-3)=0  x = 3, 

(x+1)= 0 x = -1  (cannot use)

3hr = time second tank would take alone, first tank 6hr alone

checking our answer

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