You are walking down a straight path in a park and notice there is another person walking some distance ahead of you. The distance between the two of you remains the same, so you deduce that you are walking at the same speed of 1.17 m/s. Suddenly, you notice a wallet on the ground. You pick it up and realize it belongs to the person in front of you. To catch up, you start running at a speed of 2.75 m/s. It takes you 10.5 s to catch up and deliver the lost wallet. How far ahead of you was this person when you started running

16.6 m

Explanation:

Let d be the distance the other person is ahead of you. Since the other person is walking at a speed, v = 1.17 m/s, after picking the wallet, the other person moves a distance , vt in time, t = 10.5 s, the total distance covered by you till catch up is D = d + vt.

Also, you moves with a speed of v' = 2.75 m/s in time t = 10.5 s as you pick up the wallet, you covers a distance d' = v't at catch up.

At catch up, D = d'

d + vt = v't

d = v't - vt

d = (v' - v)t

Substituting the values of the variables into d, we have

d = (2.75 m/s - 1.17 m/s)10.5 s

d = (1.58 m/s)10.5 s

d = 16.59 m

d ≅ 16.6 m

So, the other person was 16.6 m ahead of you when you started running.