Question

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?

Answer 1

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 `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

`1/7 + 1/5 = 12/35`

To determine how many hours they need to complete the train, find a number that multiplied with `12/35` will give you `35/35 = 1`.

`12/35 * x = 1 implies x= 35/12 ~= 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 `"2 hours"` and `"55 minutes"`.