SOLUTION: a tank fitted with two pipes is to be filled with water. One pipe can fill it in 15 hours. After it has been open for 3 hours, the second pipe is opened and the tank is filled in 4

Algebra ->  Rate-of-work-word-problems -> SOLUTION: a tank fitted with two pipes is to be filled with water. One pipe can fill it in 15 hours. After it has been open for 3 hours, the second pipe is opened and the tank is filled in 4      Log On


   

Question 916972: a tank fitted with two pipes is to be filled with water. One pipe can fill it in 15 hours. After it has been open for 3 hours, the second pipe is opened and the tank is filled in 4 hours more. How long would it take the second pipe alone to fill the tank
Answer by mananth(16946) About Me  (Show Source):
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a tank fitted with two pipes is to be filled with water. One pipe can fill it in 15 hours. After it has been open for 3 hours, the second pipe is opened and the tank is filled in 4 hours more. How long would it take the second pipe alone to fill the tank

One pipe can fill it in 15 hours.
it does 1/15 of the job in 1 hour

After it has been open for 3 hours,
In 3 hours it does 3/15 of the job
Balance job = 1-3/15
=12/15 of the job
the second pipe is opened and the tank is filled in 4 hours more.
12/15 of the job they do in 4 hours
1 job they do in 4/(12/15)
=5 hours
let second pipe take x hours to fill the tank
it does 1/x of the job in 1 hour
First pipe does 1/15 of the job in 1 hour
together they do 1/5 of the job in 1 hour
1/15 +1/x = 1/5
1/5 -1/15 =1/x
2/15 = 1/x
x= 15/2
=7.5 hours
the second pipe alone to fill the tank will take 7.5 hours