document.write( "Question 765630: two athelets P and Q are running around a circular track of 1200m at speeds of 6mps and 3mps respectively.Both of them start from the same point in the same direction but P reverses his direction every time he completes one round.After how much time from the start will they meet for the first time? \n" ); document.write( "
Algebra.Com's Answer #466299 by Theo(13342)\"\" \"About 
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as far as i can tell, they will meet at the 800 meter mark.
\n" ); document.write( "they both start at the 0 meter mark.
\n" ); document.write( "p is going at 6 meters per second and q is going at 3 meters per second.
\n" ); document.write( "p will be at the 1200 meter mark in 200 seconds.
\n" ); document.write( "q will be at the 600 meter mark in 200 second.
\n" ); document.write( "p reverses his direction.
\n" ); document.write( "they are now 600 meters apart.
\n" ); document.write( "since they are running towards each other their rates will be additive.
\n" ); document.write( "the formula is rate * time = distance.
\n" ); document.write( "the distance is 600 meters.
\n" ); document.write( "the formula becomes:
\n" ); document.write( "(r1 + r2) * time = distance
\n" ); document.write( "this formula becomes:
\n" ); document.write( "(6m/s + 3m/s) * time = 600m
\n" ); document.write( "simplify to get:
\n" ); document.write( "9m/s * time = 600m
\n" ); document.write( "divide both sides by 9m/s to get:
\n" ); document.write( "time = 600m / (9m/s) which becomes:
\n" ); document.write( "time = 600m * (s/9m) which then simplifies to:
\n" ); document.write( "time = 66.6666667 seconds
\n" ); document.write( "the total distance traveled is 600 meters in 66.6666667 seconds.
\n" ); document.write( "p will have traveled 66.6666667 * 6 = 400 meters in 66.6666667 seconds.
\n" ); document.write( "q will have traveled 66.6666667 * 3e = 200 meters in 66.666667 seconds.
\n" ); document.write( "p is going backwards from the 1200 meter mark to the 800 meter mark.
\n" ); document.write( "p is going forward from the 600 meter mark to the 800 meter mark.
\n" ); document.write( "they will meet at the 800 meter mark.
\n" ); document.write( "total time traveled is 200 + 66.6666667 seconds.
\n" ); document.write( "in 200 seconds, p has gone forward from the 0 meter mark to the 1200 meter mark.
\n" ); document.write( "in another 66.6666667 seconds, p has gone backwards from the 1200 meter mark to the 800 meter mark.
\n" ); document.write( "in 200 seconds, q has gone forward from the 0 meter mark to the 600 meter mark.
\n" ); document.write( "in another 66.6666667 seconds, q has continued to go forward from the 600 meter mark to the 800 meter mark.\r
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