3 pumps were used to empty a pond hold an unknown amount of water. If pump 1 can empty it in 4 days, pump 2 in 10 days and #3 in 5 days, how many days will it take to empty the pond if all 3 are running at the same time?
Let x = time (days) for all 3
then
x(1/4 + 1/10 + 1/5) = 1
multiplying both sides by 20
x(5 + 2 + 4) = 20
x(11) = 20
x = 20/11
x = 1.82 days
or
x = 1 day, 19 hours and 38 minutes
To find out how many days it would take to empty the pond if all three pumps are running at the same time, we need to find the rate at which each pump empties the pond per day.
Let's denote the rate at which pump 1 empties the pond as R1 (in pond per day), pump 2 as R2, and pump 3 as R3.
From the given information, we know that pump 1 empties the pond in 4 days, pump 2 in 10 days, and pump 3 in 5 days. Therefore, we can calculate the rates as follows:
R1 = 1/4 pond per day (since it empties the pond in 4 days)
R2 = 1/10 pond per day (since it empties the pond in 10 days)
R3 = 1/5 pond per day (since it empties the pond in 5 days)
Now, to find the combined rate at which all three pumps empty the pond, we add up their individual rates:
Combined rate = R1 + R2 + R3
= 1/4 + 1/10 + 1/5 pond per day
= 5/20 + 2/20 + 4/20 pond per day
= 11/20 pond per day
So, the combined rate at which all three pumps empty the pond is 11/20 pond per day.
Finally, to find the number of days it would take to empty the pond, we can divide the total volume of the pond by the combined rate:
Number of days = Total volume of pond / Combined rate
Since the total volume of the pond is unknown, it is not possible to determine the exact number of days it would take to empty the pond with the given information.