Question

Jim and his dad are bricklayers. Jim can lay bricks for a fireplace and chimney in 5 days. With his father's help he can build it in 2 days. How long would it take his father to build it alone?

Answer 1

we are given

Jim can lay bricks for a fireplace and chimney in 5 days

Jim's 1 day work is

`=(1)/(5)`

we are given

With his father's help he can build it in 2 days

so, both can do same work in 2 days

so, both's 1 day work is

`=(1)/(2)`

Let's assume

his father to build it alone in x days

his father 1 day work is

`=(1)/(x)`

so, both's 1 days work is

`=(1)/(x)+(1)/(5)`

so, we can set it to 1/2

we get

`(1)/(2)=(1)/(x)+(1)/(5)`

now, we can solve for x

`(1)/(2)=(5*1)/(5*x)+(1*x)/(5*x)`

`(1)/(2)=(5+x)/(5x)`

now, we can cross multiply

`5x=2(5+x)`

`5x=10+2x`

`3x=10`

now, we can solve for x

`x=(10)/(3)`

so,

his father to build it alone is

`=(10)/(3)days`............Answer