Tom took a trip of 1,300 miles. he traveled by train at 50 miles an hour and the same number of hours by plane at 275 mph. how many hours did the trip take?

  8 hours

Step-by-step explanation:

Since the times are the same at each speed, the ratio of distances traveled at each speed is the ratio of the speeds:

  distance at 50 : distance at 275 = 50 : 275 = 2 : 11

The sum of distances is 1300 mi, and the sum of ratio units is 13, so each must stand for a distance of 100 miles. That is, Tom traveled 200 miles at 50 miles per hour and 1100 miles at 275 miles per hour.

The portion of the trip at 50 mph took ...

  200 mi/(50 mi/h) = 4 h

Since this is the same time as the other portion of the trip, the entire trip took 8 hours.

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