SOLUTION: Hi Particles X and Y are set to collide with each other at a certain time.they are 250m away from each other on a straight line path. X leaves point A for point B and Y leaves p

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Question 1162119: Hi
Particles X and Y are set to collide with each other at a certain time.they are 250m away from each other on a straight line path. X leaves point A for point B and Y leaves point B for point A. If A leaves earlier by 2.5 min the two particles will collide 3.5min after Y leaves point B. If Y leaves earlier by 2.5min they will collide 4min after X leaves point A .Find the average speeds of both particles.
Thanks


Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


"If X (not A) leaves earlier by 2.5 min the two particles will collide 3.5 min after Y leaves point B"

Translation: X traveling for 3.5+2.5 = 6 minutes, plus Y traveling for 3.5 minutes, covers the whole 250m.

6x%2B3.5y+=+250

"If Y leaves earlier by 2.5 min they will collide 4 min after X leaves point A"

Translation: X traveling for 4 minutes, plus Y traveling for 4+2.5 = 6.5 minutes, covers the whole 250m.

4x%2B6.5y+=+250

Solve the pair of equations using elimination. Multiply the first equation by 2 and the second by 3 and subtract to eliminate x:

12x%2B7y+=+500
12x%2B19.5y+=+750
12.5y+=+250
y+=+250%2F12.5+=+20

y = 20; substitute in any of the earlier equations to find x=30.

ANSWER: The speed of particle X is 30m/min; the speed of particle Y is 20m/min