Question 1207782
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1.  Suppose that you have entered an 87-mile biathlon that consists of a run and a bicycle race. 
During your run, your average speed is 6 miles per hour, and during your bicycle race, 
your average speed is 25 miles per hour. You finish the race in 5 hours. 
What is the distance of the run? What is the distance of the bicycle race?
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<pre>
Let "t" be the time running, in hours.

Then the time cycling is (5-t) hours.


The total distance equation is 

    6t + 25(5-t) = 87  miles.


Simplify and find "t"

    6t + 125 - 25t = 87,

     125 - 87 = 25t - 6t

         38   =    19t

          t    =    38/19 = 2 hours.


So, you run 2 hours and cycle 5-2 = 3 hours.


The distance running is  6*2 = 12 miles.  The distance cycling is 25*3 = 75 miles.    <U>ANSWER</U>
</pre>

Solved.



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2.  In the 1984 Olympics, C.Lewis of the United States won the gold medal in the 100-meter race 
with a time of 9.99 seconds. In the 1896 Olympics,Thomas Burke,also of the United States, 
won the gold medal in the 100-meter race in 12.0 seconds. 
If they ran in the same race repeating their respective times, by how many meters would Lewis beat Burke?
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<pre>
C.Lewis finished  12 - 9.99 = 2.01 seconds ahead of Thomas Burke.


Hence, C.Lewis beat Burke by  {{{2.01*(100/12.0)}}} = 16.75 meters.    <U>ANSWER</U>


Here the ratio  {{{100/12.0}}}  is the Burke' average speed in meters per second.
</pre>

Solved.