Question 478507
a small pipe takes 4 more hours to fill a pool than a larger pipe.
 the 2 pipes were opened at the same time to fill a pool with water.
after 3 hours, the larger pipe was closed. it took 2 more hours for a smaller pipe to complete filling up the pool.
 How many hours will be needed for each pipe to fill the pool alone?
:
Let x = time required by the large pipe alone
then
(x+4) = time required by the small pipe
:
Let completed job = 1; (a full pool)
:
From the information given we know the large pipe was on for 3 hrs & the small pipe for 5 hrs
:
{{{3/x}}} + {{{5/((x+4))}}} = 1
multiply each side x(x+4), results
3(x+4) + 5x = x(x+4)
3x + 12 + 5x = x^2 + 4x
8x + 12 = x^2 + 4x
0 = x^2 + 4x - 8x - 12
A quadratic equation
x^2 - 4x - 12 = 0
Factors to 
(x-6)(x+2) = 0
The positive solution
x = 6 hrs for large pipe to fill the pool alone
then
6 + 4 = 10 hrs for the small pipe to do it
:
:
See if this adds up
3/6 + 5/10 = 1