Question 674181
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Hi,
The 6-horsepower pump requires 5 hours more than the 10horsepower pump to empty the pool when working by itself
10horsepower pump {{{highlight(x)}}}
6-horsepower pump {{{highlight(x+5)}}}
PER hr KEY: emptied in 6 hours using both
Using both Algebraically
{{{ 1/x + 1/(x+5) = 1/6 }}} |Multiplying thru by 6x(x+5) so as all denominators = 1
 6(x+5) + 6x = x(x+5)
 6x + 30 + 6x = x^2 + 5x
   x^2 - 7x - 30 = 0
factoring
(x+3)(x-10) = 0   ||x = 10hr, time it would take the 10hp by itself
Note: Negative solution is tossed out for unit measrement