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

168 minutes

Explanation:

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

This means that in 1 minute the first person cleans
`\[(1)/(120)\]` 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
`\[(1)/(x)\]` of the tank.

Working together, the two persons clean,

`\[(1)/(120) + (1)/(x)\]` 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
`\[(1)/(70)\]` of the tank.

Expressing in equation form:

`\[(1)/(120) + (1)/(x) = (1)/(70)\]`

`\[=> (1)/(x) = (1)/(70) - (1)/(120) \]`

`\[=> (1)/(x) = (12-7)/(840) \]`

`\[=> (1)/(x) = (5)/(840) \]`

`\[=> (1)/(x) = (1)/(168) \]`

`\[=> x = 168 \]`

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