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Answer :
Answer:
Rate of the Eastbound train is 93 mph.
Step-by-step explanation:
Let the speed of the Eastbound train = x miles per hour
And the speed of the West bound train = y mph
Eastbound train travels 14 mph slower than the westbound train,
So the equation will be,
y - x = 14 ----------(1)
If these trains are 400 miles apart after 2 hours,
Distance traveled by the Eastbound train = Speed × Time
= 2x miles
Distance traveled by the Westbound train = 2y miles
Trains are 400 miles apart after 2 hours,
So the equation will be,
2y + 2x = 400
x + y = 200 ----------(2)
By adding equation (1) and equation (2)
(y - x) + (x + y) = 14 + 200
2y = 214
y = 107 mph
From equation (1)
107 - x = 14
x = 107 - 14
x = 93 mph
Therefore, rate of the Eastbound train is 93 mph.
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Final answer:
The rate of the eastbound train is 93 miles per hour, obtained by setting up an equation to represent the total distance covered by both trains in 2 hours and solving for the unknown speed.
Explanation:
The question involves determining the rate of the eastbound train given that it is 14 miles per hour slower than the westbound train and after 2 hours, both trains are 400 miles apart. To solve this, we can set up an equation where the sum of the distances traveled by both trains in 2 hours amounts to 400 miles.
Let the speed of the eastbound train be x miles per hour. Therefore, the speed of the westbound train will be x + 14 miles per hour. Since distance is equal to speed multiplied by time, the eastbound train travels 2x miles in 2 hours, and the westbound train travels 2(x + 14) miles in the same time.
The sum of these distances is equal to the total separation between the trains, which is 400 miles: 2x + 2(x + 14) = 400. Simplifying this equation, we get 4x + 28 = 400, and then 4x = 372. Dividing both sides by 4, we find that x = 93. Therefore, the rate of the eastbound train is 93 miles per hour.
