Question 1162119
<br>
"If X (not A) leaves earlier by 2.5 min the two particles will collide 3.5 min after Y leaves point B"<br>
Translation: X traveling for 3.5+2.5 = 6 minutes, plus Y traveling for 3.5 minutes, covers the whole 250m.<br>
{{{6x+3.5y = 250}}}<br>
"If Y leaves earlier by 2.5 min they will collide 4 min after X leaves point A"<br>
Translation: X traveling for 4 minutes, plus Y traveling for 4+2.5 = 6.5 minutes, covers the whole 250m.<br>
{{{4x+6.5y = 250}}}<br>
Solve the pair of equations using elimination.  Multiply the first equation by 2 and the second by 3 and subtract to eliminate x:<br>
{{{12x+7y = 500}}}
{{{12x+19.5y = 750}}}
{{{12.5y = 250}}}
{{{y = 250/12.5 = 20}}}<br>
y = 20; substitute in any of the earlier equations to find x=30.<br>
ANSWER: The speed of particle X is 30m/min; the speed of particle Y is 20m/min<br>