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Question 817747: The first pipe alone can fill a water tank in 3 hours. If a second pipe is opened to fill the same tank together with the first pipe, it will take 45 minutes to fill the tank. How long will it take the second pipe to fill the tank alone?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! R1 is the rate of pipe 1
R2 is the rate of pipe 2
when the pipes are both filling the tank together, their rates are additive.
pipe 1 fills the tank i 3 hours.
this means that pipe 1 fills 1/3 of the tank per hour.
R1 is therefore equals to 1/3.
pipe 1 and pipe2, working together, fill the tank in 3/4 of an hour.
this means that pipe 1 and pipe 2, working together, fill 4/3 of the tank per hour.
since, when pipe 1 and pipe 2 are working together, their rates are additive, then this means that R1 + R2 = 4/3
you now have 2 equations.
R1 = 1/3
R1 + R2 = 4/3
substitute 1/3 for R1 in the second equation and you get:
1/3 + R2 = 4/3
subtract 1/3 from both sides of this equation to get:
R2 = 4/3 - 1/3 which is equal to (4-1) / 3 which is equal to 3/3 which is equal to 1.
this means that R2 is equal to 1.
this means that R2, working alone, would fill the rank in 1 hour.
let's see if that holds up.
we are told that pipe 2 and pipe 2, working together fill the tank in 3/4 of an hour.
the formula is R * T = Q
R is the rate of work.
T is the time
Q is the quantity.
for pipe 1 alone, R = 1/3 and Q = 1, so the formula becomes:
1/3 * T = 1
solve for T to get T = 3 hours.
for pipe 2 alone, R = 1 and Q = 1, so the formula becomes:
1 * T = 1
solve for T to get T = 1
when they work together, their rates are additive.
formula becomes:
(R1 + R2) * T = Q
R1 + R2 = 1 + 1/3 = 4/3
Q = 1
formula becomes:
4/3 * T = 1
multiply both sides of this equation by 3/4 and you get:
3/4 * 4/3 * T = 3/4 * 1
simplify to get:
T = 3/4
solution to this problem is:
pipe 2 alone can fill the tank in 1 hour.
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