This is a proportion problem and the given information allows us to formulate the equation below:
42 trains/18 hours = x/12 hours
where x is the number of trains that pass near Emma’s house in 12 hours. We can solve this equation by first cross multiplying.
18 hours × x = 42 trains × 12 hours
Carrying out the product on the right-hand side, we get:
18 hours × x = 504 trains·hours
We can solve for x by dividing both sides of the equation by 18 hours.
(18 hours × x)/18 hours = 504 trains·hours/18 hours
Carrying out the division, we get a 1 on the left-hand side and a 28 on the right-hand side.
1x= 28 trains
We can drop the 1 next to x, to get x= 28 trains. In 12 hours, 28 trains pass near Emma’s house.