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Answer :
Answer:
The rate of the eastbound train is 68 miles per hour.
Step-by-step explanation:
It is given that two trains leave the station at the same time, one heading east and the other west.
The eastbound train travels 14 miles per hour slower than the westbound train.
Let the rate of westbound train be x and the rate of eastbound train be x-14.
Distance covered by trains in 4 hours,
Westbound train = 4x
Eastbound train = 4(x-14)
The two trains are 600 miles apart after 4 hours.
[tex]4x+4(x-14)=600[/tex]
[tex]4x+4x-56=600[/tex]
Add 56 on both sides.
[tex]8x=600+56[/tex]
[tex]8x=656[/tex]
Divide both sides by 8.
[tex]x=82[/tex]
The rate of westbound train = 82.
The rate of eastbound train = x-14 = 82-14 = 68
Therefore the rate of the eastbound train is 68 miles per hour.
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Final answer:
The speed of the eastbound train is 143 mph.
Explanation:
Let's define the speed of the westbound train as W miles per hour. Thus, the speed of the eastbound train will be W - 14 miles per hour. As the trains are moving in opposite directions, their combined speed is W + (W - 14) mph. Given that the two trains are 600 miles apart after 4 hours, we can set up the equation 4(W + W - 14) = 600 to find the speed of the westbound train. Solving this equation gives W = 157 mph. Then, the speed of the eastbound train is 157 - 14 = 143 mph.
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