Two trains are capable of traveling at speeds of 60 km/hr and 40 km/hr on parallel tracks. When they move towards each other, they pass by in 12 seconds. However, when they are moving in the same direction, a passenger in the faster train notices that they overtake the other train in 36 seconds. What are the lengths of the trains?

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60 and 120 meters

60 and 180 meters

Correct

60 and 240 meters

120 and 180 meters

180 and 1440 meters

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Explanation

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Official Explanation

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Let's analyze the two scenarios. First, in the second scenario, the passenger in the faster train is effectively a point that travels the length of the slower train in 36 seconds. Therefore, the length of the slower train can be calculated using the relative speed of the two trains moving in the same direction. The relative speed is (60 - 40) km/hr, which equals 20 km/hr. This translates to

\frac{20000}{3600} = \frac{50}{9}

m per second, or approximately 5.56 m/s. Over 36 seconds, the distance…

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What this question tests

What it tests

Your application of distance = rate × time to trains, boats, and commuters, including relative speed.

Common trap

Mixing units (miles per hour vs. minutes) or averaging speeds — average speed is total distance over total time.