Question 201710
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If a race car can go around a track in 5 minutes, then how long will it take to go around the track 
if it increases its speed by 20%?
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This problem is simple - so, the solution must be simple and short.



<pre>
Let  'd'  be the circumference (the length from start to finish).  It is not given in the problem.

Let  'v'  be the average speed of the car.


We are given that the travel time is 5 minutes.  It means

    {{{d/v}}} = 5 minutes.


Now 'v'  increases by 20%.  The new speed is now 1.2v, and they want you evaluate  {{{d/(1.2v)}}}.


We write  

    {{{d/(1.2*v)}}} = {{{(1/1.2)*(d/v)}}} = we replace here {{{d/v}}} by 5 and continue =

             = {{{5/1.2}}} = 4.16161616...  minutes  (infinite periodical decimal fraction)


So, the answer is  4.16161616...  minutes.


5 minutes is the same as 5*60 = 300 seconds,  so, in seconds, the new travel time is  

    {{{300/1.2}}} = 250 seconds, or 4 minutes and 10 seconds.
</pre>

Thus the problem is solved completely, with explanations accessible to a beginner student.


I showed you a formal way to solve, but much shorter than @Theo's explanations in his post.



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Another way reasoning is THIS:


<pre>
    The speed increased in 1.2 times, the distance remained the same - - - hence, the time decreased in 1.2 times.

    So, the new time is  {{{5/1.2}}} minutes = 4.16161616... minutes = 4 minutes and 10 seconds.
</pre>

Thus, you have two ways to build your solution: one way is formal, another way is informal and short.


You should understand both ways.  They both are elementary.