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Answer :
Final answer:
To find the rate of the westbound train, we set up an equation based on the total distance covered by both trains in 5 hours, which is 900 miles. After solving the equation, the rate of the westbound train is found to be 83 miles per hour.
Explanation:
The student is asking how to find the rate of the westbound train if two trains leave the station at the same time, one heading west and the other east, and the westbound train travels 14 miles per hour slower than the eastbound train.
After 5 hours, they are 900 miles apart. To solve for the westbound train's rate, we'll start by letting 'x' represent the speed of the eastbound train in miles per hour. Consequently, the westbound train's speed will be 'x - 14' mph.
The total distance covered by both trains after 5 hours is 900 miles. Since they're moving in opposite directions, we can add their distances to get the total distance.
The distance traveled by the eastbound train is 5x miles, and that for the westbound train is 5(x - 14) miles. Thus, the equation we can set up is:
5x + 5(x - 14) = 900
Solving this equation:
- 5x + 5x - 70 = 900
- 10x - 70 = 900
- 10x = 900 + 70
- 10x = 970
- x = 97 (Eastbound train's speed in mph)
- Westbound train's speed = x - 14 = 97 - 14
Westbound train's speed = 83 mph
Therefore, the rate/speed of the westbound train is 83 miles per hour
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Answer:
The answer to your question is 166 mi/h
Step-by-step explanation:
Data
ve = rate eastbound train
vw = rate westbound train = ve - 14
distance = d = 900 mi
time = t = 5 h
Formula
v = [tex]\frac{distance}{time} = \frac{d}{t}[/tex]
Substitution and simplification
[tex]ve = \frac{900}{5} = 180 mi/h[/tex]
Now, substitute this value in the equation of vw
vw = 180 - 14
Result
vw = 166 mi/h
