Question

Two persons work together at the local aquarium. It takes the first person 120 minutes to clean the jellyfish tanks. Since the second person is new to the​ job, it takes him longer to perform the same task. When working​ together, they can perform the task in 70 minutes. How long does it take the second person to do the task by​ himself?

Answer 1

Answer:

168 minutes

Step-by-step explanation:

It takes 120 minutes for the first person to clean the jellyfish tank.

This means that in 1 minute the first person cleans $\[\frac{1}{120}\]$ of the tank.

Let the time taken by the second person working alone to clean the tank be x minutes.

Then in 1 minute the second person cleans $\[\frac{1}{x}\]$ of the tank.

Working together, the two persons clean,

$\[\frac{1}{120} + \frac{1}{x}\]$ of the tank

But it is given that the two persons working together can clean the tank in 70 minutes. This means that in 1 minute both of them can clean $\[\frac{1}{70}\]$ of the tank.

Expressing in equation form:

$\[\frac{1}{120} + \frac{1}{x} = \frac{1}{70}\]$

$\[=> \frac{1}{x} = \frac{1}{70} - \frac{1}{120} \]$

$\[=> \frac{1}{x} = \frac{12-7}{840} \]$

$\[=> \frac{1}{x} = \frac{5}{840} \]$

$\[=> \frac{1}{x} = \frac{1}{168} \]$

$\[=> x = 168 \]$

This means that the second person can clean the tank in 168 minutes.