Question

Two trains leave the station at the same time, one heading west and the other east. The westbound train travels 10 miles per hour slower than the eastbound train. If the two trains are 400 miles apart after 2 hours, what is the rate of the westbound train?

Answer 1

the rate of the westbound train is 95 miles per hour.

Explanation:

Let's denote the rate of the eastbound train as "x" miles per hour. Since the westbound train travels 10 miles per hour slower, its rate can be represented as "x - 10" miles per hour.We know that the total distance covered by both trains after 2 hours is 400 miles.The eastbound train covers a distance of 2x miles in 2 hours.

The westbound train covers a distance of 2(x - 10) miles in 2 hours.Since the total distance covered is 400 miles, we can set up the equation:2x + 2(x - 10) = 400Simplifying the equation:2x + 2x - 20 = 400

4x - 20 = 400

4x = 420

x = 105

Therefore, the rate of the eastbound train is 105 miles per hour.To find the rate of the westbound train, we substitute this value back into the expression "x - 10":Rate of the westbound train = 105 - 10 = 95 miles per hour.Hence, the rate of the westbound train is 95 miles per hour.