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Tuesday, August 13, 2013

Word Problem - Race Problem

Category: Algebra, Physics, Mechanics

"Published in Newark, California, USA"

In a 100-meter race, Pepito gives Willie a 30-meter start and losses by 2 ½  seconds. In the second trial, he gives Willie a 10-meter start and beats him by 2 ½ seconds. Find the rate of each runner.

Solution:

The given word problem above is about a marathon or race problem. Let's analyze the word problem as follows:

Let x = be the rate of Willie
      y = be the rate of Pepito
       t = total time of Pepito to finish the 100-meter race

If the first statement says "In a 100-meter race, Pepito gives Willie a 30-meter start and losses by 2 ½  seconds.", then the working equation will be


 
Note:


If the second statement says "In the second trial, he gives Willie a 10-meter start and beats him by 2 ½ seconds.", then the working equation will be



Equate the first equation with the second equation because the two cases or trials are both in a 100-meter race










Substitute the value of x to either of the two equations above, we have









Hence, the value of y will be equal to



Therefore, the final answers are

Rate of Pepito = y = 5 meters per seconds
Rate of Willie =  x = 4 meters per seconds