Father can paint the fence of their garden in 2 hours working alone. his son, alone, can paint the fence in 3.5 hours. how long will it take them to paint the fence together?

Father and son will paint a fence together in 1.2727 hours

Solution:

Given that  

Number of hours taken by Father to paint a fence alone = 2 hours  

Number of hours taken by Son to paint a same fence alone = 3.5 hours

Need to determine how much hours will be taken to paint the same fence when both father and son work together.

Let assume the work of painting the fence is represented by "x"

Work done by father alone in 2 hours = x

Work done by father alone in 1 hour =

Work done by son alone in 3.5 hours = x

Work done by son alone in 1 hour =

work done in 1 hour by father and son together = Work done by father alone in 1 hour + Work done by son alone in 1 hour

Number of hours required when working together is given as:

Hence father and son working together will paint a fence in 1.2727 hours.

(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