very simple question

G

Guest

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Here is a simple question that's bothering me because my two friends got different answers from mine!
Ok, here it is:

At a constant rate flow it takes 20 min. to fill a swimming pool if a large hose is used, and 30 min. if a small hose is used. At these constant rates, how many minutes will it take to fill the pool when both hoses are used simultaneously?
My answer: 10 min. :? I just substracted 20 from 30 min.
My friends' answers: 12 and 13.33!!!
What would be your answer guys?
Thank you for your help :p
 
Consider the following:

1--A can paint the house in 5 hours.
2--B can paint the house in 3 hours.
3--A's rate of painting is 1 house per A hours (5 hours) or 1/A (1/5) houses/hour.
4--B's rate of painting is 1 house per B hours (3 hours) or 1/B (1/3) houses/hour.
5--Their combined rate of painting is 1/A + 1/B (1/5 + 1/3) = (A+B)/AB (8/15) houses /hour.
6--Therefore, the time required for both of them to paint the 1 house is 1 house/(A+B)/AB houses/hour = AB/(A+B) = 5(3)/(5+3) = 15/8 hours = 1 hour-52.5 minutes.

Note - T = AB/(A + B), where AB/(A + B) is one half the harmonic mean of the individual times, A and B.
 
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