at opposite ends of a 100 meter track heading toward each other Mervin moves at a rate of 5.5 mps, Leela moves at a rate of 3.2 mps, how long does it take for them to collide?

Answer 1

distance = rate x time.

total distance = 100 meters = d_M + d_L (Mervin's distance + Leela's distance)

100 = r_M x t_M + r_L x t_L

100 = 5.5t_M + 3.2t_L but the two will meet when their respective times are equal, so t_M = t_L

100 = 5.5t_M + 3.2t_M

100 = 8.7t_M

t_M = t_L = 11.494 sec.

Mervin will have gone 11.494 x 5.5 = 63.22 m; Leela will have gone 11.494 x 3.2 = 36.78 m.

Another way to think about this is using the inverse of the ratios of the two rates.

5.5/3.2 = 1.71875, so Melvin will go 1.71875 times as far as Leela in the same time (1.71875:1)

So 100/(1.71875 + 1) = 100/2.71875 = 36.78 meters for Leela, etc.