Question 1207363
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A car travelled from Kago to Agra at an average speed of 60kmlh and returned at 45km/h 
on the Same Route. If the total time taken for the joumey was 3hours 30minutes. 
Find the distance between Kaga and Agra.
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<pre>
           Method 1 - using time equation


Let "d" be one way distance, in kilometers.

Then the time moving from K to A is  {{{d/60}}}  hours;

     the time moving from A to K is  {{{d/45}}}  hours.


Total time is 3{{{1/2}}}  hours;  so we write this "time equation"

    {{{d/60}}} + {{{d/45}}} = 3{{{1/2}}}.


To solve it and to find "d", multiply both sides by 180. You will get

    3d + 4d = 630

       7d   = 630

        d   = 630/7 = 90.


<U>ANSWER</U>.  The distance is 90 km.



           Method 2 - using distance equation


Let "t" be one the travel time from K to A, in hours.

Then the travel time back is 3.5-t hours.


The distance from K to A is  60t kilometers.

The distance from A to K is  45(3.5-t) kilometers.

The distance is the same, so we write this distance equation

    60t = 45(3.5-t).


Simplify and find t

    60t = 45*3.5 - 45t

    60t + 45t = 45*3.5

       105t   = 45*3.5

          t   = {{{(45*3.5)/105}}} = 1.5.


Thus, the travel time from K to A is 1.5 hours - hence, the distance is 1.5*60 = 90 kilometers.

You get the same answer.
</pre>

Solved in two ways - for your better understanding.