Question 1183698
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A certain journey took 40min to complete. If half the distance was travelled at an average speed of 100km per hour 
and the other half at an average speed of 60km per hour, what was the length of the journey.
Thanks
Textbook says its 24km.
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<pre>
Let d be the length of the journey, in kilometers (the value under the problem's question).


Then half of the distance is  {{{d/2}}}  kilometers.


The travel time for the first  half of the distance was  {{{d/(2*100)}}}  hours.

The travel time for the second half of the distance was  {{{d/(2*60)}}}  hours.

The total time is 40 minutes,  or  {{{2/3}}}  of an hour  (GIVEN).


It gives the "time" equation


    {{{d/(2*100)}}} + {{{d/(2*60)}}} = {{{2/3}}}  of an hour.


To solve the equation, multiply both sides by 600.  You will get


    3d + 5d = 2*200

      8d    = 400

       d    = 400/8 = 50 kilometers.      <U>ANSWER</U>


<U>CHECK</U>.  1-st half of the journey takes  {{{25/100}}} = {{{1/4}}}  of an hour = 15 minutes.

        2-nd half of the journey takes  {{{25/60}}} of an hour = 25 minutes.

        Total travel time is the sum  15 minutes + 25 minutes = 40 minutes, showing my answer/solution is CORRECT.
</pre>

Solved.



The answer &nbsp;&nbsp;" 24 kilometers " &nbsp;&nbsp;from the textbook is &nbsp;&nbsp;<U>W R O N G</U>.