Question

The junior senator can do a labyrinth in 50 minutes. The senior senator can do a labyrinth in 30 minutes. Working together, how many minutes would it take them to work their way through 12 labyrinths?

Answer 1

`225\:\text{minutes}`

Explanation:

To navigate through this problem, start by finding how much each senator can complete in a fixed amount of time. I'll choose 10 as it's the greatest common factor of 30 and 50.

In 10 minutes, the junior senator can complete
`(10)/(50)=(1)/(5)` of the labyrinth.

In 10 minutes, the senior senator can complete
`(10)/(30)=(1)/(3)` of the labyrinth.

Therefore, working together, they can complete
`(1)/(5)+(1)/(3)=(8)/(15)` of the labyrinth in 10 minutes. Thus, it will take them
`(15)/(8)\cdot 10 \text{ minutes}=18.75\:\text{minutes}` to complete one labyrinth.

The amount of time it take them to complete 12 labyrinths is then
`18.75\cdot 12 =\boxed{225\:\text{minutes}}`