Physics racing question?

Question

Two runners start simultaneously from the same point on a circular track of length 185 m and run in the same direction. One runs at a constant speed of 5.50 m/s and the other at a constant speed of 6.50 m/s .

A: When will the fast one lap the slower one?

B: How far from the starting point will the slower one have run?

C: How far from the starting point will the fast one have run?

Thanks in advance guys :D

Answer 1

Two runners start simultaneously from the same point on a circular track of length 185 m and run in the same direction. One runs at a constant speed of 5.50 m/s and the other at a constant speed of 6.50 m/s. And the question is When will the fast one lap the slower one?

Let V1=6.5m/s, V2 =5.5m/s, S = 185m and
t= the time when runner1 lap runner2
then

V1t = D1 and V2t = D2

D1 will be equal to some integer number of laps around the circle plus some additional incremental distance d1, and

D2 will also be some integer number of laps around the circle plus some additional incremental distance d2. So,

V1t = nS + d1
V2t = mS + d2

In this case we want d1 = d2, so that runner1 lap runner 2, hence

(V1-V2)t = (n-m)S + (d1-d2)

but d1-d2 = 0 at time t, where runner1 lap runner2, so (V1-V2)t = (n-m)S

Now substitute the numbers in, we get:

(6.5-5.5)t = (n-m)185, or

t = (n-m)185, for m =0 and n=1 which is the smallest values of m and n we can select that corresponds to when runner1 laps runner2 the first time (i.e. runner1 will lap runner2 many times if they continues to run around the track).

A. When will the fast one lap the slower one?

At t = 185 sec is when runner1 laps runner2 the first time.

B: How far from the starting point will the slower one have run?

V2t = (5.5)(185) = 1017.5 m

C: How far from the starting point will the fast one have run?

V1t = (6.5)(185) = 1202.5 m

Answer 2

fast runner gains 1.0 m/s, so time to gain one lap = 185/1 =185s

slower runner will go 5.5 x 185 m

faster will go 6.5 x 185 m

Answer 3

what are they racing for? distance or time, laps etc...