Question

One pump can empty a pool in 3 days, whereas a second pump can empty the pool in 14 days. How long will it take the two pumps, working together, to empty the pool?

Answer 1

Answer-

It will take approximately 2.47 days for the two pumps to empty the pool when working together.

Work-

To find out how long it will take the two pumps to empty the pool together, you can use the concept of rates.

The first pump can empty 1/3 of the pool per day (since it takes 3 days to empty the pool), and the second pump can empty 1/14 of the pool per day (since it takes 14 days to empty the pool).

When they work together, you simply add their rates:

1/3 + 1/14 = 14/42 + 3/42 = 17/42

So, together, the two pumps can empty 17/42 of the pool per day.

Now, to find out how many days it will take them to empty the entire pool working together, you can take the reciprocal of their combined rate:

1 / (17/42) = 42/17 ≈ 2.47 days

So, it will take approximately 2.47 days for the two pumps to empty the pool when working together.

Answer 2

Answer: Approximately 2.470588 days

Step-by-step explanation

Let's say the pool has a capacity of 4200 gallons. Why this number? Because 3*14 = 42. Then I tacked on a couple of zeros at the end to make the capacity feel more realistic for a pool size. As you'll see in a moment, this value is used to avoid decimal results after dividing. It turns out that the capacity can be any value you want, and we'll still reach the same final answer.

One pump empties the 4200 gallon pool in 3 days. The drain rate is 4200/3 = 1400 gallons per day when working alone. The other pump drains the entire pool in 14 days. The second pump has a drain rate of 4200/14 = 300 gallons per day when working alone.

Their combined drain rate is 1400+300 = 1700 gallons per day. This assumes neither pump hinders the other.

Therefore, it would take about 4200/1700 = 2.470588 days to fully drain the pool if both pumps are working together. Round this approximate value however needed.

The relevant formulas used were:

rate = (amount drained)/(time)

time = (amount drained)/(rate)