The intake pipe can fill a certain tank in 6 hours when the outlet pipe is closed, but when the outlet pipe is open it takes 9 hours. how long would it take the outlet pipe to empty a full tank?

18 hours

Step-by-step explanation:

The unit rate of intake pipe is  [1 tank in 6 hours]

The total unit rate (combined) when 2 work together is  [1 tank in 9 hours]

Intake fills up and outlet empties. Thus we can say:

Rate of Intake - Rate of Outlet = Combined Rate

This becomes:

Where x is the rate of outlet pipe [what we are looking for]

Doing algebra we solve for x:

This means "outlet pipe can empty 3 tanks in 54 hours". So that would mean 54/3 = 18 hours to empty 1 tank

(x3 + 6x2 + 2x - 6) • (x - 1)

step-by-step explanation:

polynomial long division :

3.2     polynomial long division

dividing :   x4+5x3-4x2-8x+6

                              ("dividend")

by         :     x-1     ("divisor")

dividend     x4   +   5x3   -   4x2   -   8x   +   6

- divisor   * x3     x4   -   x3            

remainder         6x3   -   4x2   -   8x   +   6

- divisor   * 6x2         6x3   -   6x2        

remainder             2x2   -   8x   +   6

- divisor   * 2x1             2x2   -   2x    

remainder               -   6x   +   6

- divisor   * -6x0               -   6x   +   6

remainder                     0

quotient :   x3+6x2+2x-6   remainder:   0

n

step-by-step explanation: