Averaging 30 Miles Per Hour
Date: 03/17/97 at 17:58:41 From: by way of Sarah Seastone Subject: How to Average 30 MPH You go on a car trip. For half the distance, you travel at 15 mph. What speed should you travel for the rest of your trip such that you average 30 mph? Hint: Don't assume the obvious! Thanks for your help. Michelle
Date: 03/18/97 at 17:21:24 From: Doctor Anthony Subject: Re: How to Average 30 MPH Suppose half the distance is x. Time = dist/speed = x/15 Then for the second half of the journey, Time = x/v (v = speed on second half) Total time = x/15 + x/v Total distance = 2x Average speed for whole journey = Total dist/Total time = 2x/(x/15 + x/v) = 2/(1/15 + 1/v) and this must equal 30. So 2/(1/15 + 1/v) = 30 1/15 = 1/15 + 1/v 0 = 1/v so v = infinity This shows that you would require an infinite speed on the second half of the journey to get an average speed of 30 mph. -Doctor Anthony, The Math Forum Check out our web site! http://mathforum.org/dr.math/
Date: 03/18/97 at 14:16:03 From: Doctor Trent Subject: Re: Word Problem You can't do it, the trip you ask for is impossible. Let's answer this without algebra by looking at an example. Assume that you drove that first half in exactly one hour. That means you went 15 miles. The second half of the trip is then another 15 miles, for a total of 30 miles. To average 30 miles per hour, you have to finish the whole 30 miles in one hour, but you've already used up an hour, so you have no time left to travel the other 15 miles. This example would work with any time that you put in; one hour was just the simplest. You're right, don't assume! -Doctor Trent, The Math Forum Check out our web site! http://mathforum.org/dr.math/
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