Answer:
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.
