SOLUTION: Pkease help solve this problem : One pipe an fill a tank in 5 hours less than another. Together they can fill the tank in 5 hours. How long would it take each alone to fill the ta

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Question 1074980: Pkease help solve this problem : One pipe an fill a tank in 5 hours less than another. Together they
can fill the tank in 5 hours. How long would it take each alone to fill the tank ? Compute the answer
to two decimal places.
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
x, the time for one of the pipes to fill the tank
x-5, time for other pipe to fill tank

1%2Fx%2B1%2F%28x-5%29=1%2F5

.
.
x=%2815%2B5sqrt%285%29%29%2F2, time for the slow pipe; about 13.09 hours.
About 8.09 hours for the fast pipe alone to fill tank

Answer by ikleyn(52787) About Me  (Show Source):
You can put this solution on YOUR website!
.
Let x = time in hours for the faster pipe to fill the tank alone.
Then the time for the other pipe is (x+5) hours.

The faster pipe fills 1%2Fx of the tank volume per hour.
The slower pipe fills 1%2F%28x%2B5%29 of the tank volume per hour.

Working together, they fill 1%2Fx+%2B+1%2F%28x%2B5%29 of the tank volume per hour.

According to the condition,

1%2Fx+%2B+1%2F%28x%2B5%29 = 1%2F5.

It is your equation to solve.
The first step is to multiply both sides by 5x*(x+5). You will get

5(x+5) + 5x = x*(x+5),   or

5x + 25 + 5x = x^2 + 5x,

x^2 - 5x - 25 = 0.

x%5B1%2C2%5D = %285+%2B-+sqrt+%2825+%2B+4%2A25%29%29%2F2 = %285+%2B-+5%2Asqrt%285%29%29%2F2.

x%5B1%5D = %285+%2B+5%2Asqrt%285%29%29%2F2 = 8.1 hours (approximately).

The second root is negative and doesn't work.


Check.  1%2F8.1+%2B+1%2F%288.1%2B5%29 = 0.2.  Correct !


Answer. Faster pipe in 8.1 hours. Slower pipe in 13.1 hours.

Solved.

For a wide variety of similar solved joint-work problems with detailed explanations see the lessons
    - Using Fractions to solve word problems on joint work
    - Solving more complicated word problems on joint work
    - Selected joint-work word problems from the archive
    - Using quadratic equations to solve word problems on joint work (*)
in this site.

Read them and get be trained in solving joint-work problems.

Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this textbook under the topic "Rate of work and joint work problems" of the section "Word problems".


The lesson in the list marked by (*) contains other similar solved problems relevant to yours.