Question 1138422
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A bus travelling 200 km has 10 stages at equal {{{highlight(cross(interval))}}} <U>lengths</U>. 
The speed of the bus in the various stages was observed to be 10, 15, 20, 25, 20, 30, 40, 50, 30, 40 {{{highlight(kilometers)}}} per hour. 
Find the average speed at which the bus travels?
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<pre>
Each interval is  {{{200/10}}} = 20 kilometers long and the time for each interval is

    {{{20/10}}}  hours  for the 1-st interval

    {{{20/15}}}  hours  for the 2-nd interval

    {{{20/20}}}  hours  for the 3-rd interval

    {{{20/25}}}  hours  for the 4-rd interval

      .  .  .  .  and so on  .  .  .  . 


So, the total time is


    Total time = {{{20*(1/10 + 1/15 + 1/20 + 1/25 + 1/20 + 1/30 + 1/40 + 1/50 + 1/30 + 1/40)}}} = 


        the common denominator is  600;  so, I am continuing 


    = {{{20*(60/600 + 40/600 + 30/600 + 24/600 + 30/600 + 20/600 + 15/600 + 12/600 + 20/600 + 15/600)}}} = 


    {{{20*((20 + 40 + 30 + 24 + 30 + 20 + 15 + 12 + 20 + 15)/600)}}} = {{{20*(226/600)}}} = {{{226/30}}} hours.


Then the average speed = {{{total_distance/total_time}}} = {{{200/((226/30))}}} = {{{(200*30)/226}}} = {{{(100*30)/113}}} = {{{3000/113}}} = 23.077 kilometers per hour.       <U>ANSWER</U>
</pre>

Solved and completed.