Question

Two joggers are running with constant speed in opposite directions around a circular lake. One jogger runs at a speed of 2.15 m/s; The other runs at a speed of 2.55 m/s. The track around the lake is 300m long, and the two joggers pass each other at exactly 3:00 PM. How long is it before the next time the two joggers pass each other again?

Answer 1

The two joggers will pass each other after 1 minute and 4 seconds at 3:01:04 PM.

Step-by-step explanation:

The situation is analogous to two joggers running in opposite direction in a straight line where one jogger starts at the beginning of the line and the other starts at the other end, 300 m ahead.

The equation for the position of the joggers will be:

x = x0 + v · t

Where:

x = position of the jogger at time t

x0 = initial position

v = velocity

t = time

When the joggers pass each other, their position will be the same. Let´s find at which time both joggers pass each other:

x jogger 1 = x jogger 2

0 m + 2.15 m/s · t = 300 m - 2.55 m/s · t

(notice that the velocity of the joggers has to be of opposite sign because they are running in opposite directions).

2.15 m/s · t + 2.55 m/s · t = 300 m

4.70 m/s · t = 300 m

t = 300 m / 4.70 m/s = 63.8 s

The two joggers will pass each other after 1 minute and 4 seconds at 3:01:04 PM.