How long will it take for the two trains to meet?

Question

Two trains leave stations 384 miles apart at the same time and travel toward each other. One train travels at 75 miles per hour while the other travels at 85 miles per hour. How long will it take for the two trains to meet?

Answer 1

The formula needed to solve this equation is D=R*T where D is the distance traveled, R is the rate of travel and T represents the time required to travel the distance.

Since the two trains are approaching each other, the rate of approach is the sum of their speeds. They both will have traveled the same time when they meet. These facts lead to the following:

384 miles = (75 + 85 mph) * T

384 miles = 160 mph * T

T = 384 miles /160 mph = 2.4 hours

Answer 2

Since they are travelling towards each other, we just need to compute the amount of hours it would take for both of them to accumulate 384 miles.

Let x be the number of hours.

One train travels 75x miles in x hours and the other train travels 85x miles in hours so both travel 75x + 85x in x hours.

If they together they travel 384 miles, then 75x + 85x = 384 and x = 2.4 hours.