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Question 677157: A large and a small heating unit are being used to heat the water of a pool. The large unit, working alone, requires 7 h to heat the pool. After both units have been operating for 3 h, the larger unit is turned off. The small unit requires 9 h more to heat the pool. How long would it take the small unit, working alone, to heat the pool
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! A large and a small heating unit are being used to heat the water of a pool.
The large unit, working alone, requires 7 h to heat the pool.
After both units have been operating for 3 h, the larger unit is turned off.
The small unit requires 9 h more to heat the pool.
How long would it take the small unit, working alone, to heat the pool
:
let s = time required by the small unit to heat the pool alone
let the completed job = 1; (a warm pool)
:
A shared work equation; the small unit was on for 3 + 9 = 12 hrs
:
 +  = 1
multiply by 7s to clear the denominators, resulting in:
3s + 7(12) = 7s
84 = 7s - 3s
84 = 4s
s = 84/4
s = 21 hrs, the small unit working alone
;
:
Check this:
3/7 + 12/21 =
9/21 + 12/21 = 21/21 = 1
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