Question

an aquarium tank can hold 6000 liters of water. there are two pipes that can be used to fill the tank. the first pipe alone can fill the tank in 40 minutes. the second pipe can fill the tank in 60 minutes by itself. when both pipes are working together, how long does it take them to fill the tank?

Explanation:

Step1: Find rates of each pipe

The first pipe fills 6000 liters in 40 minutes, so its rate is $\frac{6000}{40} = 150$ liters per minute. The second pipe fills 6000 liters in 60 minutes, so its rate is $\frac{6000}{60} = 100$ liters per minute.

Step2: Combined rate of both pipes

When working together, their combined rate is $150 + 100 = 250$ liters per minute.

Step3: Time to fill the tank together

To find the time to fill 6000 liters at 250 liters per minute, we use $time = \frac{volume}{rate}$, so $time = \frac{6000}{250} = 24$ minutes. Alternatively, using work - rate formula (let the work be 1 tank filled): The rate of the first pipe is $\frac{1}{40}$ tanks per minute, the rate of the second pipe is $\frac{1}{60}$ tanks per minute. Combined rate $r=\frac{1}{40}+\frac{1}{60}=\frac{3 + 2}{120}=\frac{5}{120}=\frac{1}{24}$ tanks per minute. Then time $t=\frac{1}{r}=24$ minutes.

Answer:

24