A swimming pool can be emptied in 6 hours using a 10-horsepower pump along with a 6-horsepower pump. The 6-horsepower pump requires 5 hours more than the 10-horsepower pump to empty the pool when working by itself. How long will it take to empty the pool using just the 10-horsepower pump?

 10 hours

Step-by-step explanation:

The 10hp pump takes x hours to empty the pool which means it gets of the job done in one hour.

The 6hp pump takes x+5 hours to empty the pool which means it gets of the job done in one hour.  

Together, they can get of the job done in one hour.

It is given that together they get the job done in 6 hours which means they get of the job done in one hour.

10 hp pump + 6 hp pump = Together

Multiply by 6x(x+5) to eliminate the denominator:

Simplify and solve for x:

6(x + 5) + 6x = x(x + 5)

6x +  30 + 6x = x² + 5x

       12x + 30 = x² + 5x

                  0 = x² - 7x - 30

                  0 = (x - 10)(x + 3)

                  0 = x - 10         0 = x + 3

                  10 = x             -3 = x

Since the number of hours cannot be negative, disregard x = -3.

So, the only valid answer is x = 10.

none of the above.

for one of the equations to be used in the process, there has to be a term in the equation since squared is .

since there is only a term in the first equation, we cannot derive a from completing the square.

solving with completing the square