Relative Rates

[lin.peng.2013]

Chapter 3 Guide 5 page 55

Can someone explain to me the logic behind why we add when two people or things decrease the distance between themselves?

For example, one is traveling at 5 mph and another travels at 6 mph, the rate is 5 mph + 6 mph = 11mph .

Should it be minus since they are decreasing?

Thank you!

[tommywallach]

Hey Lin,

Your way of thinking about it is incorrect. The important split is not between the distance between things decreasing or increasing. It's between whether the two things are moving in the same or opposite directions.

Any time two things are moving TOWARDS each other, you add the rates. This is only logical, because they are both actively working to decrease the distance between themselves.

Any time two things are moving in the SAME direction, you subtract the rates to determine the rate at which the distance between the two things is EITHER increasing OR decreasing.

To illustrate this second example, imagine I'm running 2 mph, and you're running 3mph IN THE SAME DIRECTION. If I'm 5 miles ahead when we start, it will take you 5 hours to catch up, because you're "catch-up rate" is 1mph. Similarly, if YOU are 5 miles ahead when we start, then the distance between us will increase by 1 mile every hour.

Hope that helps!

-t