SOLUTION: Two trains leave the station at the same time, one heading west and the other east. The westbound train travels
16
miles per hour slower than the eastbound train. If the two tra
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-> SOLUTION: Two trains leave the station at the same time, one heading west and the other east. The westbound train travels
16
miles per hour slower than the eastbound train. If the two tra
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Question 1119319: Two trains leave the station at the same time, one heading west and the other east. The westbound train travels
16
miles per hour slower than the eastbound train. If the two trains are
950
miles apart after
5
hours, what is the rate of the westbound train?
Found 3 solutions by ikleyn, greenestamps, josgarithmetic:Answer by ikleyn(52800) (Show Source):
Let x be the rate of the westbound train, in miles per hour (the value under the question).
Then the rate of the eastbound train is (x+16) mph, according to the condition.
Next, the condition says that
5x + 5*(x+16) = 950.
Simplify and solve for x.
5x + 5x + 80 = 950,
10x = 950 - 80 = 870.
x = = 87 mph.
Answer. The rate of the westbound train is 87 mph.
Check. 5*87 + 5*(87+16) = 950. ! Correct !
The two trains are traveling in opposite directions for 5 hours, ending up 950 miles apart, so their combined speed is 950/5 = 190 mph.
Let the speeds be x and x+16; then any of a number of paths using basic algebra will show the two speeds are 87 mph and 103 mph.
I will show you my favorite way of getting to this answer; it might not be a method you find to your liking....
We have two speeds that combine to 190 mph; one is 16 mph faster than the other.
So we can reason that if the two speeds were the same, they would both be 190/2 = 95 mph. But since the speeds differ by 16 mph, we can get the actual speeds by adding 8 mph to one speed and subtracting 8 mph from the other. That gives the two speeds as 95+8 = 103 mph and 95-8 = 87 mph.
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