SOLUTION: A passenger train leaves a train station on schedule. A freight train had departed from the same station 2hours before the passenger taron. The passenger train is headed in the sam

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Question 1197978: A passenger train leaves a train station on schedule. A freight train had departed from the same station 2hours before the passenger taron. The passenger train is headed in the same direction as the freight train at an average speed of 16km/hr. The passenger train catches up with the freight train in 4hours and overtakes it. Calculate speed of the freight train
Found 3 solutions by Theo, greenestamps, MathTherapy:
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
when the passenger train catches up to to the freight train, they have both traveled the same distance from the train station.
the passenger train is traveling at 16 mph and catches up to the freight train in 4 hours.
16 * 4 = 64 which means the passenger train has caught up to the freight train in 64 kilometers.
the freight train travels the same distance in 6 hours, because the freight train started 2 hours before the passenger train.
64 / 6 = 10 + 2/3 kilometers per hour which is equal to 32/3 kilometers per hour.
the passenger train travels 64 kilometers in 4 hours at 16 kilometers per hour.
the freight train travels 64 kilometers in 6 hours at 32 / 3 kilometers per hour.
the speed of the freight train is 32/3 kilometers per hour.
in decimal format, that's 10.67 kilometers per hour rounded to 2 decimal places.


Answer by greenestamps(13198)   (Show Source): You can put this solution on YOUR website!


At the time when the passenger train has caught up with the freight train, the distances the two trains have traveled are the same.

At that time, the passenger train has been traveling for 4 hours and the freight train has been traveling for 6 hours.

The distances are the same, and the ratio of times is 6:4 = 3:2; that means the ratio of speeds is 2:3. So the speed of the freight train is 2/3 the speed of the passenger train.

ANSWER: 16*(2/3) = 32/3 km/hr
Answer by MathTherapy(10551)   (Show Source): You can put this solution on YOUR website!

A passenger train leaves a train station on schedule. A freight train had departed from the same station 2hours before the passenger taron. The passenger train is headed in the same direction as the freight train at an average speed of 16km/hr. The passenger train catches up with the freight train in 4hours and overtakes it. Calculate speed of the freight train
Since passenger train's speed was 16 km/h, and it caught up to the freight train 4 hours after departing, then catch-up distance = 16(4) = 64 km

As the freight train left 2 hours before the passenger train, and the passenger train caught up in 4 hours, then when the passenger
train caught up, it had been traveling for 4 + 2, or 6 hours.

Freight train's speed is therefore:

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