Running Problem (Time and Distance)
Date: 8/31/96 at 18:53:20 From: Anonymous Subject: Time and distance problems If Lucy runs 3 mph and Jan runs 7 mph, when will Jan catch up with Lucy if she gives Lucy a head start? I think I solved it with a proportion, but I wonder if this is the best approach. Here is my "solution": 3 mph : 7mph = x minutes : x + 10 minutes 3x + 30 minutes = 7x 30 minutes = 4x 7.5 minutes = x 17.5 minutes = x + 10 minutes Jan will catch up with Lucy 17.5 minutes after Lucy begins to run.
Date: 9/5/96 at 10:3:26 From: Doctor Jerry Subject: Re: Time and distance problems From your answer, the head start must be 10 minutes, or 1/6 hour. Right? Solving problems by proportion is a very nice method, but you must be certain that the method fits. It doesn't fit here, because of the head start. Imagine a number line, with both girls starting to run to the right from the 0 mark. At the time Jan starts, Lucy will be at the 3*(10/60) = 1/2 mile mark. Let a clock start running just as Lucy reaches the 1/2 mile mark. Let t be the clock time in hours. Lucy will be at the 1/2 + 3t mark and Jan will be at the 7t mark when the clock reads t hours. To find out when Jan catches up, we look for the t for which 1/2 + 3t = 7t. I'm sure you can solve this equation for t. Remember that t is measured in hours. -Doctor Jerry, The Math Forum Check out our web site! http://mathforum.org/dr.math/
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