A train leaves the train station at noon and travels at a constant speed of vt = 50 mi/hr on a straight track. 2 hr later, a car leaves the same train station and travels in the same direction at vc = 70 mi/hr on a road next to the train track. How far from the station is the place where the car catches up with the train? x =

350 miles

Explanation:

When the car starts 2 hours later, the train would have a head start of

50 * 2 = 100 miles

The speed of the car relative to the train is

70 - 50 = 20 mi/hr

For the car to catch up with the train, it must cover the 100 miles difference at the rate of 20mi/hr. So the time it would need to cover this difference is

100 / 20 = 5 hours

After 5 hours, the car would have traveled a distance of

5 * 70 = 350 miles which is also the distance from the station to where the car catches up