Trains A and B are traveling in the same direction on parallel tracks. Train A i

Question

Trains A and B are traveling in the same direction on parallel tracks. Train A is traveling at 100 miles per hour and train B is traveling at 120 miles per hour. Train A passes a station at 4:25 P.M. If train B passes the same station at 4:40 P.M., at what time will train B catch up to train A?

Explanation / Answer

4:40 pm - 4:25 pm = 15 minutes = .25 hr When train B passes the station at 4:40 pm, 15 minutes after trainA passes the station at 4:25 pm, train A is     (.25 hr)(100 mi/hr) = 25 miles ahead of train B. The two trains will meet when they are bothat the same distance from the station. The followingequations represent this scenario:     Train A's distance from the station after 4:40pm: (100 mi/hr)t + 25 mi, where t is measured in hours         Train B's distance from the station after 4:40pm: (120 mi/hr)t     Solve (100 mi/hr)t + 25 mi = (120 mi/hr)t for t:     100t + 25 = 120t =>     120t - 100t = 25 =>     20t = 25 =>     t = 25/20 = 5/4 = 1.25 hours     4:40 pm + 1.25 hours = 6:05pm The two trains will meet at 6:05pm. Check: After 1 hour, train A will be     (1 hr)(100 mi/hr) + 25 mi = 125 miles from the station, while train B will be     (1 hr)(120 mi/hr) = 120 miles from the station. After 15 more minutes, train A will be     125 mi + (.25 hr)(100 mi/hr) = 125 mi + 25mi = 150 miles from the station and train B will be     120 mi + (.25 hr)(120 mi/hr) = 120 mi + 30 mi =150 miles from the station. If you find this post helpful, please rate it.

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