Emil and Henri are playing on a soccer field that is 90m x 120m. Suppose Emil starts from the goal at one end of the field and Henri starts at the other. They run towards each other with Emil running at a rate of 3.5 meters per second and Henri running at a rate of 2.5 meters per second. How much time will pass before they meet?

Question

Emil and Henri are playing on a soccer field that is 90m x 120m.  Suppose Emil starts from the goal at one end of the field and Henri starts at the other.  They run towards each other with Emil running at a rate of 3.5 meters per second and Henri running at a rate of 2.5 meters per second.  How much time will pass before they meet?

anonymous · Answer

They start 120 meters apart from each other (the lenght of the soccer field).

Suppose Emil starts from point 0 with velocity v = 3.5 m/s
Henri starts at point 120 on our axis with the velocity v = -2.5 m/s ... cause, he is running in the other direction. You could also turn it around - it makes no difference. They meet, when they are at the same distance from Emil's (or Henri's) goal.

so $$0 + 3.5 t = 120 - 2.5 t$$
bring the t's to one side..
$$6t = 120$$
and divide by 6
$$t = 20$$

They will therefore meet after 20 seconds.