Find the speed
Linh is driving at 60 km/h on a long straight highway parallel to a train track. Every 10 minutes, she is passed by a train travelling in the same direction as she is. These trains depart from the station behind her every 3 minutes and all travel at the same constant speed. What is the constant speed of the trains, in km/h?
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1 solution
Suppose that the trains are travelling at "v km/h". Consider two consecutive points in time at which the car is passed by a train. Since these points are 10 minutes apart, and 10 minutes equals 1/6 hour, and the car travelsat 60 km/h, then the car travels: (60 km/h) · (1/6 h) = 10 km. During these 10 minutes, each train travels 1/6v km, since its speed is v km/h. At the first instance, Train A and the car are next to each other. At this time, Train B is “3 minutes” behind Train A.
Since 3 minutes is 1/20 hour, then Train B is 1/20 v km behind Train A and the car. Therefore, the distance from the location of Train B at the first instance to the location where it passes the car is ( 1/20 v + 10) km. But this distance also equals 1/6 v km, since Train B travels for 10 minutes. Thus, 1/6 v = 1/20 v + 10 OR 10/60 v − 3/60 v = 10 and so 7/60 v = 10 or v = 600/7 . Therefore, the trains are travelling at 600/7 km/h.