Question 1207311
.
A car and a van were travelling to town A. The car overtook the van at Point x 
where they were 126km from town A. The car arrived at town A 3/8 hr earlier 
than the van while the van was 18km away. Find the average speed of the car and the van.
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        It is a nice entertainment problem.  To solve it, 
        you should decipher what is hidden in its condition.



<pre>
The hidden things are these two statements:

          (1)  the car spent the same time to travel 126 km,
               as the van spent to travel 126-18 = 108 km,

    and

          (2)  the van spent 3/8 of an hour to travel 18 km.



From (2), we find the average speed of the van: it is  

    the distance of 18 km divided by the time 3/8 of an hour = {{{18/((3/8)))}}} = {{{(18*8)/3}}} = 6*8 = 48 km/h.

So, half of the problem is just solved for the van. 



For the average speed of the car, {{{v[car]}}}, we write this "time equation" based on (1)

    {{{126/v[car]}}} = {{{108/48}}}.


From this equation, we find

    {{{v[car]}}} = {{{(126*48)/108}}} = 56 km/h.


At this point, the problem is just solved in full.


<U>ANSWER</U>.  The average speed of the car is 56 km/h.  The average speed of the van is 48 km/h.
</pre>

Solved.


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Re-phrasing a famous American writer O Henry,


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;the blind begin to walk and the dumb begin to see 
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;when they receive so beautiful solutions to their mathematical problems.