Question 1208615
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Mary and Murray travel respectively at x and y km/h heading directly towards each other across a distance of 240 km. 
If both start at 9 a.m. they will meet at noon. If Murray starts at 8 a.m. and Mary starts at 10 a.m. they will meet at 12:30 p.m. 
Find (x, y)
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<pre>
In the first scenario, they travel 3 hours, each.

It gives this total distance equation

    3x + 3y = 240  kilometers.


In the second scenario, Mary travels 2.5 hours, Murray travels 4.5 hours.

It gives this total distance equation

    2.5x + 4y = 240  kilometers.


So, we have this system of equations

    3x    + 3y    = 240,     (1)

    2.5x + 4.5y = 240.    (2)


To solve, from equation (1) express  y = {{{(240-3x)/3}}} = 80-x and substitute it into equation (2).  
You will get

    2.5x   + 4.5(80-x)  = 240,

    2.5x + 360 - 4.5x = 240,

    2.5x - 4.5x = 240 - 360

    -2x = -120,

      x = {{{(-120)/(-2)}}} = 60.


Then y = 80-x = 80 - 60 = 20.


<U>ANSWER</U>.  (x,y) = (60,20).
</pre>


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Normally, this problem is to be solved using system of two equations in two unknown.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;But it can be solved &nbsp;MENTALLY, &nbsp;too, &nbsp;as an arithmetic word problem, &nbsp;without using equations, 
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;and I will show the way to do it.


<pre>
In the first scenario, Mary and Murray travel 3 hours toward each other.  

Hence, their approaching rate is  240/3 = 80 kilometers per hour.


In the second scenario, Murray moves alone during 2 hours from 8 am to 10 am,
and after that, they move 2.5 hours together toward each other.

In these 2.5 hours, the distance between them decreases by 2.5*80 = 200 kilometers.


It means that the distance which Murray travels alone in 2 hours from 8:00 am  to  10:am  is 

        240-200 = 40 kilometers .


Hence, the Murray' speed is 40/2 = 20 km/h.


Then the Mary' speed is 80-20 = 60 km/h.


<U>ANSWER</U>.  Mary' speed is 60 km/h;  Murray' speed is 20 km/h.
</pre>

Solved in two different ways, for your better understanding.