SOLUTION: One hose can fill a goldfish pond in 60 minutes, and two hoses can fill the same pond in 35 minutes. How long does it take the second hose alone to fill the pond?

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Question 853638: One hose can fill a goldfish pond in 60 minutes, and two hoses can fill the same pond in 35 minutes. How long does it take the second hose alone to fill the pond?
Answer by LinnW(1048) About Me  (Show Source):
You can put this solution on YOUR website!
The first hose fills at a rate of 1/60 ponds per minute.
Let s = the rate at which the second fills in ponds per minute.
So (1/60)35 + (s)35 = 1 pond
35/60 + 35s = 1
add -35/60 to each side
35s = 1 - 35/60
35s = 25/60
Multiply each side by 1/35
s+=+25%2F60+%2A+1%2F35
s+=+25%2F%2860%2A35%29
s+=+%285%2A5%29%2F%282%2A5%2A6%2A5%2A7%29
s+=+1%2F%282%2A6%2A7%29
s+=+1%2F84
Let's verify that 1/84 is the correct rate.
(1/60 + 1/84)35 ?= 1
( 35/60 + 35/84 ) ?= 1
( (5*7)/(2*5*6) + (5*7)/(2*6*7) ) ?=1
( 7/12 + 5/12 ) ?= 1
12/12 = 1, so the rate 1/84 pools per minute checks out
so it will take 84 minutes to fill the pool with the second hose.