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A swimming pool can be filled by any of three hoses A, B or C. Hoses A and B together take 4 hours to fill the pool. Hoses A and C together take 5 hours to fill the pool. Hoses B and C together take 6 hours to fill the pool. How many hours does it take hoses A, B and C working together to fill the pool? Express your answer as a decimal to the nearest hundredth.

 Mar 20, 2020
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1/A+1/B=1/4, 1/A+1/C=1/5, 1/B+1/C=1/6, solve for A,B,C


A = 120/17 and B = 120/13 and C = 120/7


17/120 + 13/120 + 7/120 =1 / F, solve for F


F =120 / 37 =3.243 hours - or ~3 hours and 14.6 minutes to fill the pool.

 Mar 20, 2020

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