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}](https://tex.z-dn.net/?f=%5Cfrac%7BDistance%7D%7BSpeed%7D)
∵ 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
∵ ![\frac{x}{50}-\frac{x}{85}=1.4](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7B50%7D-%5Cfrac%7Bx%7D%7B85%7D%3D1.4)
- 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](https://tex.z-dn.net/?f=%5Cfrac%7B85x-50x%7D%7B%2850%29%2885%29%7D%3D1.4)
∴ ![\frac{35x}{4250}=1.4](https://tex.z-dn.net/?f=%5Cfrac%7B35x%7D%7B4250%7D%3D1.4)
- 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
Learn more:
You can learn more about the word problems in brainly.com/question/9533500
#LearnwithBrainly