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Question
Two trains travel from A to B by different routes.  One route is 15 miles longer than the other.

Shorter route- 6 hours travel time.

Longer route- 8.5 hours travel time at 10 miles less per hour.

Determine length of shorter route.

Thank you.

distance = rate × time

The train taking the shorter route travels 6 hours at v miles per hour.
length of shorter route = 6 hours × v miles/hour = 6v miles

The train taking the longer route travels 8.5 hours at (v-10) miles per hour.
length of longer route = 8.5 hours × (v-10) miles/hour = 8.5v - 85 miles

(longer route) - (shorter route) = 15 miles
(8.5v-85) - (6v) = 15
2.5v = 100
v = 40
6v = 240
The shorter route is 240 miles long.

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#### Janet Yang

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