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 Prague at 2:00 pm, averaging 30 mph.
Another train headed in the same direction leaves Prague at 4:00 pm, averaging 40 mph.
To the nearest tenth, how many hours after the second train leaves will it overtake the first train?
2.
A train leaves Oslo at 10:00 am, averaging 30 mph.
Another train headed in the same direction leaves Oslo at 2:00 pm, averaging 40 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 Barcelona at 3:00 pm, averaging 60 mph.
Another train headed in the same direction leaves Barcelona at 7:00 pm, averaging 90 mph.
To the nearest minute, at what time will the second train overtake the first train?
2.
A train leaves Kansas City at 2:00 pm, averaging 30 mph.
Another train headed in the same direction leaves Kansas City at 5:00 pm, averaging 40 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 New Dehli at 11:00 am, averaging 50 mph.
Another train headed in the opposite direction leaves New Dehli at 1:00 pm, averaging 60 mph.
To the nearest mile, how far are the two trains from each other at 2:00 pm?
2.
A train leaves Brussels at 5:00 pm, averaging 50 mph.
Another train headed in the opposite direction leaves Brussels at 6:00 pm, averaging 70 mph.
To the nearest mile, how far are the two trains from each other at 10:00 pm?

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

1.
A train leaves Brussels for a nearby city at 9:30 pm, averaging 65 mph.
Another train leaves the nearby city for Brussels at 12:30 am, averaging 90 mph.
If the nearby city is 660 miles from Brussels, to the nearest minute, at what time will the two trains pass each other?
2.
A train leaves Denver for a nearby city at 10:15 am, averaging 60 mph.
Another train leaves the nearby city for Denver at 1:00 pm, averaging 70 mph.
If the nearby city is 2765 miles from Denver, 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 Oslo at 12:45 pm, averaging 70 mph.
Another train headed in the same direction leaves Oslo at 3:15 pm, averaging 90 mph.
To the nearest tenth, how many hours after the second train leaves will it overtake the first train?
2.
A train leaves Denver at 6:15 am, averaging 45 mph.
Another train headed in the same direction leaves Denver at 10:45 am, averaging 70 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 Amsterdam at 4:15 pm, averaging 70 mph.
Another train headed in the same direction leaves Amsterdam at 8:45 pm, averaging 85 mph.
To the nearest minute, at what time will the second train overtake the first train?
2.
A train leaves Venice at 12:15 pm, averaging 50 mph.
Another train headed in the same direction leaves Venice at 2:45 pm, averaging 75 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 Cairo at 12:48 am, averaging 69 mph.
Another train headed in the opposite direction leaves Cairo at 2:30 am, averaging 83 mph.
To the nearest mile, how far are the two trains from each other at 4:30 am?
2.
A train leaves Buenos Aires at 3:46 am, averaging 61 mph.
Another train headed in the opposite direction leaves Buenos Aires at 5:15 am, averaging 71 mph.
To the nearest mile, how far are the two trains from each other at 7:15 am?
3.
A train leaves Amsterdam at 4:31 am, averaging 82 mph.
Another train headed in the same direction leaves Amsterdam at 5:15 am, averaging 93 mph.
To the nearest minute, at what time will the second train overtake the first train?

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