SOLUTION: Hi 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, wha

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Question 1183698: Hi
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.
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52786)   (Show Source): You can put this solution on YOUR website!
.
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.
~~~~~~~~~~~~~~~ 

Let d be the length of the journey, in kilometers (the value under the problem's question).


Then half of the distance is    kilometers.


The travel time for the first  half of the distance was    hours.

The travel time for the second half of the distance was    hours.

The total time is 40 minutes,  or    of an hour  (GIVEN).


It gives the "time" equation


     +  =   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.      ANSWER


CHECK.  1-st half of the journey takes   =   of an hour = 15 minutes.

        2-nd half of the journey takes   of an hour = 25 minutes.

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

Solved.


The answer   " 24 kilometers "   from the textbook is   W R O N G.



Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


Certainly the textbook answer you show is not right. 24km in 40 minutes means an average speed of (24/(2/3))=36km/h. That's not possible if the speeds for the two halves of the trip were 100km/h and 60km/h.

Here is an approach to the problem very different from the one shown by the other tutor.

The two distances are the same; the ratio of the two speeds is 100:60=5:3.

That means the times spent at the two speeds are in the ratio 3:5.

So 3/8 of the 40 minutes was spent at 100km/h and 5/8 of the 40 minutes at 60km/h. The total distance was then



ANSWER: 50km
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