City A is far from City B by 170 miles
Step-by-step explanation:
A railroad track runs parallel to a highway from City A to City B
- An express train and an automobile leave City A at the same time
- The train travels 85 mph
- The automobile travels at 50 mph
- The train arrives 1 hour and 24 minutes before the automobile arrives
We need to find how far is City A from City B
Assume that the distance from City A to City B is x mile
∵ Distance = Speed × Time
∴ Time =
∵ The speed of the train = 85 mph
∵ Distance between city A and city B = x miles
∴ The time for the train = hours
∵ The speed of the automobile = 50 mph
∵ Distance between city A and city B = x miles
∴ The time for the automobile = hours
The train takes time less because it travels by high speed
∵ The train arrives 1 hour and 24 minutes early then the automobile
- Change the time to hour only
∵ 1 hour = 60 minutes
∴ 24 minutes = hour
∴ 24 minutes = 0.4 hour
∴ The train arrives 1.4 hours early then the automobile
Now lets subtract the time of the train from the time of the automobile and equate the answer by 1.4
∵
- Multiply each numerator by the other denominator and multiply
the two denominators to make the two fraction a single fraction
∴
∴
- Multiply both sides by 4250 to cancel the denominator
∴ 35x = 5950
- Divide both sides by 35
∴ x = 170
City A is far from City B by 170 miles
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