Question

A tank can be filled with water by two pipes running together in 11 and 1/9 minutes. If the larger pipe alone takes 5 minutes less to fill the tank than the smaller pipe, find the time that each pipe will take to fill the tank.

Answer 1

Let S = number of minutes it will take the smaller pipe to fill the tank
alone.
S - 5 = numbef of minutes it will take the larger pipe to fill the tank
alone.
Therefore, 1/S = part of the tank filled by small pipe in 1minute
1/(S - 5) = part of the tank filled by larger pipe in 1 minute

(1/S) + [1/(S - 5)] = 1/(11 1/9)
(1/S)(100/9) + [1/(S - 5)](100/9) = 1

100/9S + 100/[9(S - 5)] = 1
100/S + 100/(S - 5) = 9
100(S - 5) + 100S = 9S(S - 5)
100S - 500 + 100S = 9S^2 - 45S
200S - 500 = 9S^2 - 45S
9S^2 - 45S - 200S + 500 = 0
9S^2 - 245S + 500 = 0
Using the Quadratic Formula, we have
S = 25 minutes, number of minutes for smaller pipe to fill the tank alone
L = 25 - 5 = 20 minutes, number of minutes fo larger pipe to fill the tank alone

Answer 2

Thank-you!

Answer 3

Welcome!