Math Practice Topic: Train Problems

Description: This is an SAT-level topic that applies the concept of distance = rate x time using word problems that involve trains. You may need pencil and paper.

Adaptive Learning Progression: Lots of variety, progressively becoming more difficult.

Sample Levels (out of 10)

Solve. If asked for time, a proper answer looks like this: 1:35am

1.
A train leaves Florence at 12:00 am, averaging 50 mph.
Another train headed in the same direction leaves Florence at 2:00 am, averaging 80 mph.
To the nearest tenth, how many hours after the second train leaves will it overtake the first train?
2.
A train leaves San Francisco at 9:00 am, averaging 30 mph.
Another train headed in the same direction leaves San Francisco at 10:00 am, averaging 60 mph.
To the nearest tenth, how many hours after the second train leaves will it overtake the first train?

Solve. If asked for time, a proper answer looks like this: 1:35am

1.
A train leaves Florence at 7:00 am, averaging 60 mph.
Another train headed in the same direction leaves Florence at 9:00 am, averaging 80 mph.
To the nearest minute, at what time will the second train overtake the first train?
2.
A train leaves Berlin at 4:00 pm, averaging 80 mph.
Another train headed in the same direction leaves Berlin at 7:00 pm, averaging 100 mph.
To the nearest minute, at what time will the second train overtake the first train?

Solve. If asked for time, a proper answer looks like this: 1:35am

1.
A train leaves Taipei at 9:00 pm, averaging 40 mph.
Another train headed in the opposite direction leaves Taipei at 1:00 am, averaging 60 mph.
To the nearest mile, how far are the two trains from each other at 4:00 am?
2.
A train leaves Denver at 3:00 am, averaging 70 mph.
Another train headed in the opposite direction leaves Denver at 5:00 am, averaging 80 mph.
To the nearest mile, how far are the two trains from each other at 7:00 am?

Solve. If asked for time, a proper answer looks like this: 1:35am

1.
A train leaves Kansas City for a nearby city at 9:30 am, averaging 35 mph.
Another train leaves the nearby city for Kansas City at 10:15 am, averaging 55 mph.
If the nearby city is 431.25 miles from Kansas City, to the nearest minute, at what time will the two trains pass each other?
2.
A train leaves Rome for a nearby city at 6:30 pm, averaging 30 mph.
Another train leaves the nearby city for Rome at 10:30 pm, averaging 55 mph.
If the nearby city is 375 miles from Rome, to the nearest minute, at what time will the two trains pass each other?

Solve. If asked for time, a proper answer looks like this: 1:35am

1.
A train leaves Florence at 12:45 am, averaging 100 mph.
Another train headed in the same direction leaves Florence at 3:15 am, averaging 110 mph.
To the nearest tenth, how many hours after the second train leaves will it overtake the first train?
2.
A train leaves Austin at 4:30 pm, averaging 65 mph.
Another train headed in the same direction leaves Austin at 7:30 pm, averaging 85 mph.
To the nearest tenth, how many hours after the second train leaves will it overtake the first train?

Solve. If asked for time, a proper answer looks like this: 1:35am

1.
A train leaves Buenos Aires at 12:00 pm, averaging 95 mph.
Another train headed in the same direction leaves Buenos Aires at 4:00 pm, averaging 125 mph.
To the nearest minute, at what time will the second train overtake the first train?
2.
A train leaves Denver at 7:30 pm, averaging 45 mph.
Another train headed in the same direction leaves Denver at 8:15 pm, averaging 70 mph.
To the nearest minute, at what time will the second train overtake the first train?

Solve. If asked for time, a proper answer looks like this: 1:35am

1.
A train leaves Las Vegas at 10:50 am, averaging 63 mph.
Another train headed in the same direction leaves Las Vegas at 11:00 am, averaging 91 mph.
To the nearest tenth, how many hours after the second train leaves will it overtake the first train?
2.
A train leaves Geneva at 8:38 am, averaging 48 mph.
Another train headed in the opposite direction leaves Geneva at 9:00 am, averaging 64 mph.
To the nearest mile, how far are the two trains from each other at 11:00 am?
3.
A train leaves Venice at 2:20 pm, averaging 95 mph.
Another train headed in the same direction leaves Venice at 4:30 pm, averaging 113 mph.
To the nearest tenth, how many hours after the second train leaves will it overtake the first train?

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