One pump can empty a pool in 5 days, whereas a second pump can empty the pool in 7 days. How long will it take the 2 pumps, working together, to empty the pool?
Is the answer 2 11/12 days (3 days)
Add the pumping rates in pools per day to get the combined pumping rate.
Rate = 1/5 + 1/7 = 12/35 pools per day
Time required = (1 pool)/(12/35 pool/day) = 35/12 day = 70 hours
That agrees with your answer. Don't round off 35/12 as 3 days. You will be marked wrong.
Thanks
To find the time it takes for the two pumps to empty the pool together, we need to calculate their combined rate of work.
Let's denote the rate at which the first pump empties the pool as "R1" and the rate at which the second pump empties the pool as "R2." We can calculate these rates by taking the inverse of the time it takes for each pump to empty the pool.
The first pump empties the pool in 5 days, so its rate can be calculated as 1/5 (1 pool / 5 days), and the second pump empties the pool in 7 days, so its rate is 1/7 (1 pool / 7 days).
To find the combined rate of the two pumps working together, we can add their individual rates:
Combined rate = R1 + R2 = 1/5 + 1/7
Now, we can find the time it takes for the two pumps to empty the pool together by taking the inverse of their combined rate (the combined rate of work):
Time = 1 / (Combined rate) = 1 / (1/5 + 1/7)
To simplify the calculation, we need to find the least common denominator (LCD) of 5 and 7, which is 35.
Therefore, the combined rate becomes: R1 + R2 = 7/35 + 5/35 = 12/35
Now, we can find the time it takes for the two pumps to empty the pool together:
Time = 1 / (Combined rate) = 1 / (12/35)
To divide by a fraction, we can invert the fraction and multiply:
Time = 1 * (35/12) = 35/12 = 2 11/12 days
Therefore, the answer is 2 11/12 days, or approximately 2.92 days, which can be rounded to 3 days.