Question

An experienced window washer can wash all the windows in Mike’s house in 2 hours, while a new trainee can wash all the windows in 7 hours. How long would it take them working together? Round your answer to the nearest minute if needed.

Answer 1

Answer:

It would take 1.55 hours or 93.6 minutes for them if they work together.

Solution:

Let us assume together both can complete the work in x hours.

Experienced window washer can wash the house in 2 hours.

So, in 1 hour he will do, $\frac{1}{2}$ part of the house

Hence, in x hours he will do $\frac{x}{2}$ part of the house

Again the trainee can wash all the windows in 7 hours

So, in 1 hour he will do, $\frac{1}{7}$ part of the house

Hence, in x hours he will do$\frac{x}{7}$ part of the house

We can now say,

$\Rightarrow \frac{x}{2}+\frac{x}{7}=1$

$\Rightarrow \quad x \times\left(\frac{7+2}{14}\right)=1 \\\\ \Rightarrow x \times\left(\frac{9}{14}\right)=1 \\\\ \Rightarrow x=\frac{14}{9}=1.55$

They can complete in 1.55 hours.

1 hour = 60 minutes

So, according to unitary method, $1.55 hours = 1.55\times60 \Rightarrow 93.6 minutes$.

Answer 2

The experienced window washer can wash all the windows in Mike’s house in 2 hours, which implies that in 1 hour he completes 1/2 of the job.

By the same logic, the new trainee completes 1/7 of the job in one hour.

If they work together, they complete

$\dfrac{1}{2}+\dfrac{1}{7}=\dfrac{7}{14}+\dfrac{2}{14}=\dfrac{9}{14}$

of the job in one hour, meaning that they complete the job in 14/9 of a hour.