Two pumps are filling a pool. one of them is high power and can fill the pool alone in 2 hours less time than the other can do so. given that, working together, both pumps can fill the pool in 144 minutes, how long, in hours, will it take the powerful pump to fill the pool alone?

9.1 hours

Step-by-step explanation:

Make a Chart.  

Column 1 is Time it takes to do the job alone

Column 2 is Rate of Work  ( 1 over the expression in Column 1)

Column 3 is Time it takes to do the job together

Column 4 is Part of the Job done  ( Columns 2 and 3 multiplied together )

Row 1 is the First pipes info.

Row 2 is the Second pipes info.

The equation comes from column 4.    Part of the Job from Pipe 1  +  Part of the Job from Pipe 2  =  1  (the whole job)

So Row 1 for Pipe 1, the small pipe, would look like this:    x    ,    1/x     ,    4     ,    4/x

Row 2 for Pipe 2, the larger pipe, would look like this:     x - 2  ,   1/x-2   ,   4     ,    4/(x-2)

So, the equation would be:     4/x   +   4/(x-2)    =   1

Solve this equation by first multiplying both side by  x(x-2) to clear the denominators.

So the equation becomes:  4(x-2) + 4x  = x(x-2)

Distribute and combine like terms, then get everything on one side of the equation.

So the equation becomes:   x^2  - 10x + 8  = 0

Use the quadratic equation to solve for x.  Solutions are  x = 9.1 and x = .9

.9 hours does not make sense so throw that solution out (with the dirty pipe water :) )

9.1 hours makes sense for how long it would take the smaller pipe working alone to fill the pool.

4 hours

Step-by-step explanation:

x = smaller pump fill time

y = bigger pump fill time

x = y + 120

(144 / x) + (144 / y) = 1

[144 / (y + 120)] + (144 / y) = 1

144 y + 144 y + (144 * 120) = y (y + 120)

0 = y^2 - 168 y - 17280

4 hours