Lesson Two runners run on a quarter-mile oval track

Two runners run on a quarter-mile oval track

Problem 1

          Alex will laps Kelly first time at the moment, when Alex covers the distance, which exactly one quarter mile 

          (precisely the length of the track) longer than the distance Kelly covers to this moment.



                ===--->>>  It is the key point to understand when solving such problems (!)  <<<---===



This condition takes the form of THIS equation


    10.98*t - 10.65*t = 0.25,    or


    (10.98 - 10.65)*t = 0.25,

     0.33*t = 0.25 

     t =  = 0.757576 of an hour.


At that time moment Kelly will cover  10.65*0.757576 = 8.068 miles.

So, Kelly will complete 8*4 = 32 full quarter-mile track lengths and will be at 0.068 miles from the starting point on the track.



To find the moment of the SECOND lap, we can formally determine the time when Alex will overtake/lap Kelly in two track lengths.


It leads to the similar equation, but you can complete the solution even without using equation.


Simply note that the position of the first lap now plays the role of the former starting point.



As soon as you understand it, you will guess the ANSWER: 


    ===--->>>  the second lap point is remoted 2*0.068 = 0.136 miles from the starting point.  <<<---===