# Maria can build a model train in 7 hours. Anne can build a model train in 5 hours. How long would it take them if they work together?

Aug 6, 2015

They would need 2 hours and 55 minutes.

#### Explanation:

The key to this problem is to figure out how much of the complete train the two girls can each build per hour, assuming of course that they work at a constant rate.

This will give you an idea about how much of the train they can build together per hour.

So, if Maria can build a complete train in 7 hours, then she needs 1 hour to complete $\frac{1}{7}$ of the train.

Likewise, Anne can build a complete train in 5 hours, so she needs 1 hour to complete !/5 of the train.

This means that , together, they can complete

$\frac{1}{7} + \frac{1}{5} = \frac{12}{35}$

To determine how many hours they need to complete the train, find a number that multiplied with $\frac{12}{35}$ will give you $\frac{35}{35} = 1$.

$\frac{12}{35} \cdot x = 1 \implies x = \frac{35}{12} \cong 2.92$

To express this in hours, use the fact that one hour has 60 minutes

2.92color(red)(cancel(color(black)("hours"))) * "60 minutes"/(1color(red)(cancel(color(black)("hour")))) = "175.2 minutes"

The total time will thus be $\text{2 hours}$ and $\text{55 minutes}$.