Rational Expressions

Question

One pipe can fill a pool in six hours. When two pipes are opened, they fill the pool in five hours. how long would it take to fill the pool if only the slower pipe is used?

Answer 1

For combined work problems

r₁t + r₂t = 1

If only the first pipe is open, then

r₁6 = 1 --> r₁= 1/6

If both pipes are open then it only takes 5 hours

r₁(5) + r₂(5) = 1 --> 5/6 +5r₂ = 1 -->r₂ = 1/30

For the slower pipe alone,

r₂t =t/30 = 1 --> t = 30 hours