The distance d a train travels varies directly with the amount of time t has elapsed since departure. If the train travels 475 miles in 9.5 hours, how many miles did the train travel after 4 hours?
To find the miles the train traveled after 4 hours, we first need to find the constant of variation, which relates the distance and time.
We can set up the proportion:
distance/time = distance/time
Given that the train travels 475 miles in 9.5 hours, we substitute these values into the proportion:
475 miles/9.5 hours = distance/4 hours
Cross-multiplying, we get:
475 miles * 4 hours = 9.5 hours * distance
Dividing both sides of the equation by 9.5 hours, we get:
(475 miles * 4 hours)/9.5 hours = distance
Simplifying, we get:
200 miles ≈ distance
So, the train traveled approximately 200 miles after 4 hours.