Two friends are at the local high school track, a circle measuring 440 yards for one complete lap. Abe can jog at 8.2 miles per hour while Bob’s jogging speed is 4.6 miles per hour. If they both start at the same point and jog in the same direction (say clockwise), how many times would they have crossed each other after a half hour? If they started off in opposite directions, what would your answer be?

Answer 1

s = 440 yards = 402.3 m
v1 = 8.2 mph = 3.7 m/s,
v2 = 4.6 mph = 2.1 m/s.

Imagine that B is at rest, then A is jogging at the relative velocity
v = v1-v2 =3.7 – 2.1 = 1.6 m/s.
The time of 1 lap motion is
T = s/v=402.3/1.6 =251 s.
The number if their meetings is
N = t/T =0.5•3600/251 =7.17 => 7.
When they are moving un opposite directions the relative velocity is
v = v1+v2 = 3.7 +2.1 = 5.8 m/s.
T = s/v =402.3/5.8 =69.3 s.
N =t/T =0.5•3600/69.3 = 25.9 => 25

Answer 2

Thanks a lot Elena