Question

The speed of a passenger train is 6 mph faster than the freight train. The passenger train travels 260 miles in the same time the freight train travels 230 miles. What would be the speed of both the passenger and freight trains?

Answer 1

The speed of the freight train is 46 mph and the speed of the passenger train is 52 mph.

Step-by-step explanation:

Let's assume the speed of the freight train is x mph. Since the passenger train is 6 mph faster, its speed would be x + 6 mph.

We know that the time taken by both trains is the same. Let's calculate the time taken by the freight train first.

Time = Distance / Speed

Time taken by the freight train: 230 / x hours

Time taken by the passenger train: 260 / (x + 6) hours

Since both times are the same, we can set up an equation:

230 / x = 260 / (x + 6)

Cross-multiplying, we get:

230 * (x + 6) = 260 * x

Expanding the equation, we have:

230x + 1380 = 260x

Subtracting 230x from both sides, we get:

1380 = 30x

Dividing both sides by 30, we find:

x = 46

So, the speed of the freight train is 46 mph.

The speed of the passenger train is 6 mph faster, so the passenger train's speed is 46 + 6 = 52 mph.