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Problems on Trains

A train travels at an average speed of 20 mph through urban areas, 50 mph through suburban areas, and 75 mph through rural areas. If a trip consists of traveling half an hour through urban areas, 3 1/2 hours through suburban areas, and 3 hours through rural areas, what is the train's average speed for the entire trip?
1. 50 mph
2. 53 2/7 mph
3. 54 3/7 mph
4. 58 4/7 mph

The train will average 50 mph for 31/2 hours, 75 mph for 3 hours and 20 mph for half an hour. So, the distance of the trip is (3 1/2) (50) + (3)(75) + (1/2)(20) = 175 + 225 + 10 = 410 miles. The trip takes 7 hours. Therefore, the average speed is 410/7 = 58 4/7 mph.

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