SOLUTION: Two pipes running simultaneously can fill a swimming pool in 6 hours. If both pipes run for 3 hours and the first is then shut-off, it requires 4 hours more for the second to fill
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Question 1064379: Two pipes running simultaneously can fill a swimming pool in 6 hours. If both pipes run for 3 hours and the first is then shut-off, it requires 4 hours more for the second to fill the pool. How long does it take the pipe to fill the tank if the drain is closed?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
x is the rate of the first pipe.
y is the rate of the second pipe.
rate * time = quantity of work produced.
when they work together their rates are additive
therefore, (x + y) * 6 = 1
simplify this to get 6x + 6y = 1
when they both work for 3 hours, they fill 1/2 the pool.
one of them is then shut shut and the other takes 4 hours to fill the pool.
assuming the rate of the pipe that fills half the pool in 4 hours is x, then you get:
4x = 1/2
this says that the second pipe, working at a rate of x amount of the pool in one hour, takes 4 hours to fill half the pool.
if you multiply both sides of that equation by 2, you will see that the second pipe takes 8 hours to fill the pool by itself.
to find out how long it takes the first pipe to fikll the pool by itself, you have 2 equations that need to be solved simultaneously.
they are:
6x + 6y = 1
4x = 1/2
solve for x to get x = 1/8.
replace x in the first equation with 1/8 to get 6/8 + 6y = 1
simplify to get 6/8 + 6y = 8/8
subtract 6/8 from both sides of the equation to get 6y = 2/8.
solve for y to get y = (2/8)/6 = 2/48 = 1/24
the rate of the pipe that was shut off is 1/24 of the pool in one hour.
you get x = 1/8 and y = 1/24
simplify to get x = 3/24 and y = 1/24
the combined rate is 4/24 = 1/6.
go back to the original equation to get (x + y) * y = 1 which becomes 1/6 * 6 = 1 which becomes 1 = 1.
the solution is good
the rate of the pipe that was shut off after 3 hours is 1/24 of the pool in one hour.
that rate was originally y that we solved to get y = 1/24.
the rate of the pipe that was left open to finish the job in 4 hours is 1/8 of the pool in one hour.
that rate was originally x that we solved to get x = 1/8.
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