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

Answer:

$225\:\text{minutes}$

Step-by-step 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 $\frac{10}{50}=\frac{1}{5}$ of the labyrinth.

In 10 minutes, the senior senator can complete $\frac{10}{30}=\frac{1}{3}$ of the labyrinth.

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

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