Question

Two trains are traveling towards each other. One is traveling at twice the speed of the other. They started traveling at the same time from two separate stations that are 405 miles apart. In three hours the trains pass each other. Find the rate that each train is traveling.

Answer 1

Let's call the speed of the slower train "S" (in miles per hour). Then, the speed of the faster train would be "2S" since it's traveling at twice the speed.

The total distance they need to cover to meet each other is 405 miles, and they meet in 3 hours.

Using the formula: Distance = Speed × Time, you can set up two equations based on the distance each train travels:

1. Distance covered by the slower train = Speed of slower train × Time
2. Distance covered by the faster train = Speed of faster train × Time

For the slower train:
Distance = S × 3 hours

For the faster train:
Distance = 2S × 3 hours

Since they meet after traveling the full distance between the two stations (405 miles), you can set up the equation:

Distance covered by slower train + Distance covered by faster train = Total distance
(S × 3) + (2S × 3) = 405 miles

Now, simplify and solve for S:

3S + 6S = 405

9S = 405

Now, divide both sides by 9 to find S:

S = 405 / 9

S = 45

So, the slower train is traveling at 45 miles per hour, and the faster train is traveling at twice that speed, which is 90 miles per hour.