Question 1005772: A man is three eighths of the way across a bridge when he hears a train coming from behind.
If he runs as fast as possible back toward the train, he will get off the bridge just in time to avoid a collision.
Also, if he runs as fast as possible away from the train, he will get off the bridge (on the other side) just in time to avoid a collision.
The train is traveling at 60 miles per hour. How fast does the man run?
Hi! So I sent this question already, but my email says it didn't send so I apologize if you have already seen it. Thanks for taking the time to help! Also, sorry if there are any typos!
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! THE ALGEBRA-STYLE SOLUTION:
 = length of the bridge, in miles
 = distance to cover running towards the train
 = distance to cover running away from the train
 = the man's running speed, in miles per hour
 = time (in hours) the man must run towards the train to save himself
 = time (in hours) the man must run away from the train to save himself
Running toward the train is scarier, but it will save time and effort.
The time saved, in hours is
 .
That is the time the train takes to cover the miles from one end of the bridge to the other, at  miles per hour:
 hours.
So,
 --> ---> ---> ---> .
NOTE:
If you do not need to explain step by step, you can start by writing
 .
ANOTHER WAY TO THINK OF IT:
In the time the man would have run the  of the bridge towards the train,
the train will get to the bridge.
During that time, the man can cover another of the bridge,
and be  of the way through the bridge.
While the man runs that remaining  of the bridge length,
the train at miles per hour covers the whole span of the bridge.
Since during the same time the man cover  of the distance covered by the train,
his speed must be of the speed of the train, or  .
That is a mental-math, no-need-to-show-your-work way (the one to use for a quick answer for the SAT).
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