SOLUTION: It took 3 hoses 4 hours to fill the first 20,000 gallons in a swimming pool. Then a 4th hose was added. If there was 15000 gallon left to fill, how long did it take?

Question 999687: It took 3 hoses 4 hours to fill the first 20,000 gallons in a swimming pool. Then a 4th hose was
added. If there was 15000 gallon left to fill, how long did it take?
Found 2 solutions by josgarithmetic, Theo:
Answer by josgarithmetic(39630) (Show Source): You can put this solution on YOUR website!
Not specified if each hose is pumped separately or not. One hose, four hoses, all the same. 20000 gallons in 4 hours. Fewer hoses, higher pressure.

How long to fill the last 15000 gallons?

If each hose is pumped separately but each hose works at the same rate, then the count of the hoses WILL be important, and that changes the mathematics to be used. Then, the count of the hoses affects the flow rate. Your description does not distinguish between the two types of situations.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
formula to use here would be rate per hose * number of hoses * time = quantity of water poured into the swimming pool.

since we know number of hoses and time and quantity, we can use that information to solve for rate per hose.

formula becomes:

rate per hose * 3 hoses * 4 hours = 20,000 gallons poured.

solve for rate per hose to get rate per hose = 20,000 / (3 * 4) = 20,000 / 12 = 1666.67 gallons per hour per hose.

the display is rounded.
the number i'm using is not.
that number is stored in the calculator as 1666.666666667.

the formula of rate per hose * 3 hoses * 4 hours = 20,000 gallons poured becomes:

1666.67 * 3 hoses * 4 hours = 20,000 which becomes:

20,000 = 20,000 which confirms the solution of rate per hose is correct.

we have 15,000 gallons left to pour and we are now using 4 hoses.

the same formula of rate per hose * number of hoses * time = quantity of water poured into the swimming pool is used.

this time:

rate per hose is 1666.67
number of hoses is 4
time is what we want to find.
quantity of water poured is 15,000 gallons.

formula becomes:

1666.67 * 4 * time = 15,000

we want to solve for time to get:

time = 15,000 / (1666.67 * 4) which results in:

time = 2.25 hours.

the formula becomes:

1666.67 * 4 * 2.25 = 15,000 which becomes:

15,000 = 15,000, confirming the solution is correct.

the question was how long did it take to pour in the remaining 15,000 gallons.

the solution is that it took 2.25 hours to pour in the remaining 15,000 gallons.

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