Question 121967This question is from textbook
: a mortocycle breaks down and the rider has to walk the rest of the way to work. The motorcycle was traveling at 45 mi/h, and the rider walks at a speed of 6 mi/h. The distance from home to work is 25miles, and the total time for the trip was 2 hours. How far did the motorcycle go before it broke down?
This question is from textbook
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! Let T represent the time in hours that the rider uses the motorcycle. Then, since the total
time for the trip was 2 hours, the time spent walking is 2 hours less the time on the motorcycle
... or 2 - T hours spent walking.
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Next use the fact that distance traveled is equal to the rate of travel multiplied by the amount
of time that passes for the type of transportation having that rate.
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Since the motorcycle has a rate of 45 mi/h and the amount of time that the rider uses the
motorcycle is T hours, the distance covered on the motorcycle is 45 * T miles or 45T.
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And similarly, the rider walks at 6 mi/h and the time spent walking is 2 - T hrs, the distance
covered by walking is 6*(2 - T) = 12 - 6T.
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So the total miles covered is the sum of these two distances or:
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45T + 12 - 6T
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Combine the 45T and the -6T and this expression of the total distance reduces to:
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39T + 12
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The problem tells you that the total distance is 25 miles ... so you can set the two total
distances equal to get:
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39T + 12 = 25
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Get rid of the 12 on the left side by subtracting 12 from both sides to get:
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39T = 13
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Solve for T by dividing both sides by 39 and you get:
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T = 13/39 = 1/3 hours
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But earlier we said that the distance covered by the motorcycle which travels at 45 mi/h is
45 times T. So we can say that the distance covered by the motorcycle is:
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D = 45*T = 45*(1/3) = 45/3 = 15 miles
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So the motorcycle breaks down after covering 15 miles.
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Check. Since 1/3 of an hour is spent on the motorcycle, the remainder of the 2 hours is
spent walking. And 2 hours is equal to 6/3 hours. Take 1/3 hour away from the 6/3 hours
and you find that 5/3 hours is spent walking. At the rate of 6 mi/h the distance covered
walking is:
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Distance = 6 * 5/3 = 30/3 = 10 miles
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So the rider covers 15 miles on the motorcycle and 10 miles walking for the total of 25
miles. Everything checks out.
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This means that our answer of 15 miles on the motorcycle is correct.
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Hope this helps you to see how you can work your way through this problem.
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