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

$=\frac{1}{5}$

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

$=\frac{1}{2}$

Let's assume

his father to build it alone in x days

his father 1 day work is

$=\frac{1}{x}$

so, both's 1 days work is

$=\frac{1}{x}+\frac{1}{5}$

so, we can set it to 1/2

we get

$\frac{1}{2}=\frac{1}{x}+\frac{1}{5}$

now, we can solve for x

$\frac{1}{2}=\frac{5*1}{5*x}+\frac{1*x}{5*x}$

$\frac{1}{2}=\frac{5+x}{5x}$

now, we can cross multiply

$5x=2(5+x)$

$5x=10+2x$

$3x=10$

now, we can solve for x

$x=\frac{10}{3}$

so,

his father to build it alone is

$=\frac{10}{3}days$............Answer