SOLUTION: A garden hose can fill a swimming pool in 4 days and a larger hose can fill the pool in 2 days. How long will it take to fill the pool if both the hoses are used?

Question 1042872: A garden hose can fill a swimming pool in 4 days and a larger hose can fill the pool in 2 days. How long will it take to fill the pool if both the hoses are used?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
one garden hose can fill the pool in 4 days.
the other garden hose can fill the pool in 2 days.
how long does it take if both garden hoses are used.

rate * time = quantity
rate is the amount of the pool that can be filled in one day.
time is the amount of time it takes to fill the pool
quantity is the number of pools that can be filled.
if you let r = rate and t = time and q = quantity, the formula becomes:
r*t = q

for the first hose, the formula becomes:
r * 4 = 1
rate is r
time is 4 days
quantity is 1 full pool
solve for r to get:
r = 1/4
this means that the first hose can fill 1/4 of the pool in 1 day.

for the second hose, the formula becomes:
r * 2 = 1
rate is r
time is 2 days
quantity is 1 full pool
solve for r to get:
r = 1/2
this means that the second hose can fill 1/2 of the pool in 1 day.

when they work together, their rates are additive.
rate * time = quantity becomes:
(1/2 + 1/4) * t = 1
rate is equal to (1/2 + 1/4) of the pool in one day.
time is equal to t days.
quantity is equal to 1 full pool
since 1/2 + 1/4 = 3/4, the formula becomes:
3/4 * t = 1
solve for t to get t = 4/3.
the pool can be filled in 4/3 days.

let's see if that makes sense.
the first hose is filling 1/4 of the pool in one day.
in 4/3 days, this hose fills 1/4 * 4/3 = 4/12 of the pool.

the second hose is filling 1/2 of the pool in one day.
in 4/3 days, this hose fills 1/2 * 4/3 = 4/6 of the pool.
4/6 of the pool is equal to 8/12 of the pool.

4/12 of the pool plus 8/12 of the pool equals 1 full pool at the end of 4/3 days.

your answer is it will take 4/3 days.
this can also be expressed as 1 and 1/3 days.
this can also be expressed as 1.33333.... days.

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