SOLUTION: A large and small drain are opened to drain a pool. After both drains have been opened for 1 hour, the large drain clogs, but the small remains open and requires an additional 9 ho

Question 131092: A large and small drain are opened to drain a pool. After both drains have been opened for 1 hour, the large drain clogs, but the small remains open and requires an additional 9 hours to drain the pool. The large drain alone can empty the pool in 6 hours. How long would it take the small drain to empty?
Answer by fners(16) (Show Source): You can put this solution on YOUR website!
In real life, the more water in the pool, the faster the water will drain out. However, taking this fact into account would make the problem very difficult to solve. Instead, we will assume that the water in each drain always flows at the same rate.
Say the total amount of water is x, the amount of water per hour through the small drain is a, and the amount of water through the large drain per hour is b.
We are given:
1*(b+a)+9*a=x
6*b=x
We want to find:
x/a
There are many ways to solve. Here is one:
b=x/6
1*(x/6+a)+9*a=x
x/6+a+9*a=x
x/6+10*a=x
10*a=x-x/6
10*a=x*(1-1/6)
10*a=x*5/6
60/5*a=x
12=x/a
This means 12 is the number of hours for all the water to go through the small drain.

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