Perils of Pauline-HOW FAST SHE CAN RUN?
Pauline was walking through a train tunnel on her way to town. Suddenly, she heard the whistle of a train approaching from behind her!
Pauline knew that the train always traveled at an even 60 miles per hour. She also knew that she was exactly three-eighths of the way through the tunnel. She could tell from the train whistle how far the train was from the tunnel.
Pauline wasn't sure if she should run forward as fast as she could or run back to the near end of the tunnel.
She did some lightning fast calculations, based on how fast she could run and the length of the tunnel. She figured out that whichever way she ran, she would just barely make it out of the tunnel before the train reached her. Whew!
How fast could Pauline run? How fast could Pauline run? ANSWER IN MPH
The answer is 15.
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We have this situation:
Note that neither the distance for the train to the tunnel, nor the length of the tunnel is given. Where T = length of the tunnel, P represents Pauline in Peril, ( "The Perils of Pauline") and the train is some distance, d, from the start of the tunnel. (distances in miles) Let r = Pauline's running speed in miles per minute. The train travels 1 mile per minute. Time for train to reach the start of the tunnel: d minutes Time for Pauline to reach start of the tunnel: (3/8 T) / r minutes. These are the same: d = 3/8 T / r = 3 T / 8 r Time for train to reach the end of the tunnel: d + T minutes. Time for Pauline to reach the end of the tunnel = 5 T / 8 r. These are also the same: d + T = 5 T / 8 r Substitute for d in the second equation: 3 T / 8 r + T = 5 T / 8 r Divide by T: (that means that it doesn't matter how long the tunnel is) <<<< 3 / 8r + 1 = 5 / 8r 1 = 1/4r r = 1/4 Pauline can run 1/4 mile per minute, which means she can do 4 minute miles. That's pretty quick! 15 mph. It turns out, courtesy of "M3" from Yahoo Answers, that there is a shortcut solution: Suppose that Pauline heads for the far end of the tunnel. When she has covered 3/8 of the whole tunnel (putting her at the 3/8+3/8 = 3/4 mark), the train reaches the front of the tunnel. Then Pauline covers remaining 1/4 of the tunnel, while the train covers the whole tunnel, meaning her speed is 1/4 that of the train, or 1/4 * 60 = 15 mph.