Question

Devante can shovel the driveway in 3.5 hours, but if his sister Naomi helps it would take 1.5 hours. How long would it take Naomi to shovel the driveway alone?

Answer 1

Answer: Naomi would take 2.625h to shovel the driveway.

Explanation

Given

• Devante (,d,) can shovel the driveway in 3.5 hours

,

• If his sister Naomi (,n,) helps it would take 1.5 hours.

We can rewrite the information as one job done per 3.5 hours made by Devante:

$d=\frac{1\text{ job done}}{3.5\text{ hours}}$

We do not know how much time does Naomi takes, then:

$n=\frac{1\text{ job done}}{x\text{ hours}}$

At last, together (t) they make one job done per 1.5 hours:

$t=\frac{1\text{ job done}}{1.5\text{ hours}}$

Then, we can build the relation as follows:

$\frac{1}{3.5}+\frac{1}{x}=\frac{1}{1.5}$

Multiplying everything times x:

$x\times(\frac{1}{3.5}+\frac{1}{x})=\frac{1}{1.5}\times x$$\frac{x}{3.5}+\frac{x}{x}=\frac{x}{1.5}$$\frac{x}{3.5}+1=\frac{x}{1.5}$

Grouping common terms on one side and simplifying:

$\frac{x}{1.5}-\frac{x}{3.5}=1$$x(\frac{1}{1.5}-\frac{1}{3.5})=1$$x(\frac{8}{21})=1$

Solving for x:

$x=\frac{1}{\frac{8}{21}}$$x=\frac{21}{8}=2.625$