Question 114141: One train leaves Los Angeles at 15mph heading for New York. Another train leaves from New York at 20mph heading for Los Angeles on the same track. If a bird, flying at 25mph, leaves from Los Angeles at the same time as the train and flies back and forth between the two trains until they collide, how far will the bird have traveled?
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! I think that you are missing one piece of information in this problem. You are missing the
distance between the two train stations, the one in Los Angeles and the one in New York City.
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That distance is about 2800 highway miles, so let's assume that that's the rail distance
also ... just so we can work the problem. If you later find out that the distance is different,
you can just follow the procedures, but change the numbers.
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The distance the train from Los Angeles goes until it collides with the train from New York City
is it's rate times the amount of time it takes to reach the collision point. Call that time T.
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So from departure to collision, the distance the train from Los Angeles goes is 15*T.
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Meanwhile, the train from New York City (which is assumed to depart at the same time as
the train from Los Angeles does) also travels for T hours to reach the collision point. So
its rate (20 mph) times the time T gives the distance it travels to collision.
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The two distances that the trains travel must add up to be 2800 miles. Therefore, you
can write the equation:
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15*T + 20*T = 2800 miles
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Add the two terms on the left side and you get:
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35T = 2800
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Solve for T by dividing both sides of this equation by 35 and you have:
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T = 2800/35 = 80 hours
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So from time of departure to the time of collision of the two trains is 80 hours.
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Meanwhile, during those 80 hours the bird has been flying at an average rate of 25 mph.
Therefore the distance the bird flies equals this rate times 80 hours. So the distance
that the bird covers is:
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Distance = 25*80 = 2000 miles
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The bird travels 2000 miles from the time the trains start out until the time the trains
collide.
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The confusion factor is that the bird is traveling back and forth between the trains and
your natural instinct is to figure how far the bird travels on each leg of its back and forth
trip, but that's not necessary because that was never asked. The total distance is found by
multiplying its rate times the time it takes before the trains collide.
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Hope this helps you to understand the problem and how it can be solved.
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