Question

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, but the train travels 85 mph while the automobile travels at 50 mph. If the train arrives 1 hour and 24 minutes before the automobile arrives, how far is City A from City B?

Answer 1

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 = $\frac{Distance}{Speed}$

∵ The speed of the train = 85 mph

∵ Distance between city A and city B = x miles

∴ The time for the train = $\frac{x}{85}$ hours

∵ The speed of the automobile = 50 mph

∵ Distance between city A and city B = x miles

∴ The time for the automobile = $\frac{x}{50}$ 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 = $\frac{24}{60}$ 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

∵ $\frac{x}{50}-\frac{x}{85}=1.4$

- Multiply each numerator by the other denominator and multiply

  the two denominators to make the two fraction a single fraction

∴ $\frac{85x-50x}{(50)(85)}=1.4$

∴ $\frac{35x}{4250}=1.4$

- 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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