Question

Ginger wants to fill her new swimming pool. She has two pumps; the larger pump takes 40 minutes to fill the pool, and the smaller one takes 60 minutes. How long will it take to fill the pool if both pumps are working?

Answer 1

As per the problem,

The larger pump takes 40 minutes to fill the pool.

The smaller one takes 60 minutes.

When both the pumps are working , let the time taken be x minutes , then we can write

$\frac{1}{x}=\frac{1}{40}+\frac{1}{60}\\ \\ \text{Make the denominator equal we get}\\ \\ \frac{1}{x}=\frac{1}{40}*\frac{60}{60}+\frac{1}{60}*\frac{40}{40}\\ \\ \frac{1}{x}=\frac{60}{2400}+\frac{40}{24000}\\ \\ \text{Simplify we get}\\ \\ \frac{1}{x}=\frac{60+40}{2400}\\ \\ \frac{1}{x}=\frac{100}{2400}\\ \\ \frac{1}{x}=\frac{1}{24}\\ \\ x=24$

Hence, when both the pumps works together, Time taken =24 minutes.

Answer 2

It will take one hundred minutes