Question

Towns Aburg and Bville lie 240 miles apart. The towns are connected by two parallel railroad lines. A slow and heavily laden freight train leaves on one rail line traveling from Aburg to Bville at 10 miles per hour. At the same time, the express passenger train leaves Bville for Aburg on the other line at 70 miles per hour. In how many hours will the trains just start to pass each other?

a) 2 hours
b) 3 hours
c) 4 hours
d) 5 hours

Answer 1

To find the time for two trains moving towards each other to meet, we add their speeds together to get the relative speed and then divide the distance between them by this relative speed. In this case, the trains will meet after 3 hours.

Step-by-step explanation:

To determine how many hours will the trains take to meet each other, we need to calculate the time taken for both trains to cover the distance between Aburg and Bville.

• The freight train speed: 10 miles per hour.
• The express train speed: 70 miles per hour.
• The distance between Aburg and Bville: 240 miles.

Since the trains are moving towards each other, their relative speed is the sum of their speeds. So, the relative speed is:

10 mph + 70 mph = 80 mph.

To find the time when they will meet, we divide the total distance by the relative speed:

240 miles ÷ 80 mph = 3 hours.

Therefore, the trains will start to pass each other after 3 hours, which corresponds to answer choice (b).