Using a small inlet pipe, it takes 3 hours longer to fill a pool than if a larger pipe were used.

Question

Using a small inlet pipe, it takes 3 hours longer to fill a pool than if a larger pipe were used. When both pipes are used together it takes 3.3 hours to fill the pool. Using each pipe alone, how long would it take to fill the pool? Round your answers to the nearest hour.

Answer 1

1/(3+r) + 1/r = 1/3.3

multiply by 3.3r(3+r) to eliminate fractions

3.3r + 3.3(3+r) = r(3+r)

3.3r + 9.9 +3.3r = 3r +r^2

r^2 +(3-6.6)r -9.9 = 0

r^2 -3.6r - 9.9 = 0

r = 3.6/2 + or - (1/2)sqr(3.6^2 + 4(9.9))

= 1.8 + or - (1/2)sqr52.56 = 5.42

5.42 hours for one pipe alone

8.42 hours for the other pipe alone

check the solution:

1/5.42 + 1/8.42 = 1/3.3

.18 + .12 = .3