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by resilient » Thu Mar 20, 2008 10:41 am
Tom and Linda stand at point A. Linda begins to walk in a straight line away from Tom at a constant rate of 2 miles per hour. One hour later, Tom begins to jog in a straight line in the exact opposite direction at a constant rate of 6 miles per hour. If both Tom and Linda travel indefinitely, what is the positive difference, in minutes, between the amount of time it takes Tom to cover half of the distance that Linda has covered and the amount of time it takes Tom to cover twice the distance that Linda has covered?



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108


qa is 108
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by resilient » Thu Mar 20, 2008 10:49 am
question is straightforward BUT a bit tough on setting up the equations. ANy help on setting up equations?
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by xilef » Thu Mar 20, 2008 11:10 am
rate*time=distance

Tom's distance = 6*time
Linda's distance = 2*time

Linda left 1hr earlier, so we will add 1 hr to her time


amount of time it takes Tom to cover half of the distance that Linda has covered:

6t = [2(t+1)] / 2
t=1/5 of an hr or 12 mins


amount of time it takes Tom to cover twice the distance that Linda has covered:


6t = [2(t+1)] * 2
t = 2hrs or 120 mins


the positive difference, in minutes, between the 2 times:

120 - 12 = 108 mins
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by resilient » Thu Mar 20, 2008 11:22 am
ok so the trick to the question is setting both distances equal to eachother in order to force time values! correct! THese questions are getting much easier!
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by xilef » Thu Mar 20, 2008 12:48 pm
that's right, because that is exactly what the question is asking:

amount of time it takes Tom to cover half of the distance that Linda has covered, meaning when will Tom's distance be equal to half of Linda's distance

amount of time it takes Tom to cover twice the distance that Linda has covered, meaning when will Tom's distance be equal to twice Linda's distance
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