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

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> 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       Log On


   

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) About Me  (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.