SOLUTION: A large heating unit and small heating unit are being used to heat the water of a pool The large unit, working alone, requires 8 hours to heat the pool. After both units have bee

Algebra ->  Rate-of-work-word-problems -> SOLUTION: A large heating unit and small heating unit are being used to heat the water of a pool The large unit, working alone, requires 8 hours to heat the pool. After both units have bee      Log On


   

Question 199351: A large heating unit and small heating unit are being used to heat the water of a pool The large unit, working alone, requires 8 hours to heat the pool. After both units have been working for 2 hours, the large unit is turned off. The small unit requires 7 more hours to complete the job of heating the water in the pool. How long would it take the small unit, working alone, to heat the pool water?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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A large heating unit and small heating unit are being used to heat the water
of a pool The large unit, working alone, requires 8 hours to heat the pool.
After both units have been working for 2 hours, the large unit is turned off.
The small unit requires 7 more hours to complete the job of heating the water
in the pool.
How long would it take the small unit, working alone, to heat the pool water?
:
Let x = time required by the small unit working alone
Let the completed job (heating the pool) = 1
:
Total time by the small unit: 2 + 7 = 9 hrs
2%2F8 + 9%2Fx = 1
Multiply equation by by 8x
8x*2%2F8 + 8x9%2Fx = 8x(1)
Cancel out the denominators, results:
2x + 8(9) = 8x
72 = 8x - 2x
72 = 6x
x = 72%2F6
x = 12 hrs, small unit alone
:
:
Check solution:
2/8 + 9/12 = 1