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 14.5 s to catch up and deliver the lost wallet. How far ahead of you was this person when you started running

Δx = 23.0 m

Explanation:

Since we know the time passed from the moment you picked up the wallet till you catch the other person up, and assuming that he continued moving at 1.17 m/s, we can find the distance traveled by him during this time, applying the definition of average speed, and rearrranging terms as follows:

       

Now, as we know the speed at which you started to run, assuming that the speed kept constant during all the time since you picked the wallet up, we can find the total distance till you got to deliver the wallet, as follows:

       

the distance that you were behind the other person when you started running, is just the difference between (2) and (1):Δx = x₂ - x₁ = 40.0 m - 17.0 m = 23.0 m (3)