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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
Multiply equation by by 8x
Cancel out the denominators, results:
2x + 8(9) = 8x
72 = 8x - 2x
72 = 6x
x = 12 hrs, small unit alone
2/8 + 9/12 = 1