Question about Rates & Work Strategy, Guide 4, Version 4.0

[Lamcc83]

I need clarification about pages 35 and 36 from Guide 4, World Translations, Version 4.0.

Specifically, I am not understanding when to subtract or add the rates to or from one another.

When it is stated that "Car A and Car B are driving directly toward each other," the book states that the shrinking distance between them should be represented by a+b.

Then, when it is stated in a separate problem that "Car A is chasing Car B and catching up," it is represented by the shrinking distance between them as a-b.

Lastly, when "Car A is chasing Car B and falling behind," it is represented by b-a.

Scanned PDF of problems

When do I know whether or add or subtract? I would think that if Car A is chasing Car B and Car A is falling behind, the growing distance between them would warrant addition. I don't understand the reason behind any of the problems in question.

Thanks in advance!

[RonPurewal]

Try this.

* Draw each situation. Draw a "starting line" for each car, and then draw the trajectory of each car.

* Pretend both cars are huge polluters that would spectacularly fail California's smog tests. I.e., they leave huge trails of smoke behind them.

* Draw the trails of smoke.

In the "driving toward each other" situation, note what the trails of smoke are doing. Both of them are reducing the distance between the cars.
(If you have a quantity "a + b", that shouldn't represent the distance between the cars; it should represent the combined distance that the cars have covered. I.e., the combined length of both smoke trails.)

In the "chase" situation, note that the distance in question is the difference between the two trails of smoke.

There's no sense in memorizing rules for this sort of thing"”just think about what the smoke trails are doing.

[RonPurewal]

So, yeah, the caption "Shrinking distance" isn't accurate. It should say something like "Total distance covered".

Once the cars have covered all of the distance that was originally between them"”together"”then they meet.