Question

It take Mr. Branches 5 hours to rake the leaves. If his son joins him in the work, they can rake the leaves in 3 hours. How long would it take Mr. Branches's son to rake the leaves on his own? 3 3/4 hours 6 hours 7 1/2 hours

Answer 1

Answer: 7$\frac{1}{2}$ hours

Step-by-step explanation:

Dad: $\frac{1}{5}$

Son: $\frac{1}{x}$

Together: $\frac{1}{5}$ + $\frac{1}{x}$ = $\frac{1}{3}$

                $\frac{1}{5}$(15x) + $\frac{1}{x}$(15x) = $\frac{1}{3}$(15x)

                 3x + 15 = 5x

                -3x          -3x

                        15 = 2x

                      ÷2   ÷2  

                       7.5 = x

Answer 2

Answer: 7 1/2 hours =x

Step-by-step explanation:

Hi, to answer this question we have to express the information in ratios.

Mr. Branche's time per job : 1job /5hours

MR Branches’ son = 1 job /x hours

Both = 1job/3 hours

If we add, r branches and his son's work, we obtain the total spent time by both of them.

1/5 + 1/x = 1/3

Solving for x:

1/x = 1/3 -1/5

1/x = 2/15

1 ( 2/15) =x

7 1/2 hours =x