Rate Problems

Question 1

Average Speed

Answer 1

Average speed is determined by the total distance traveled over the total time traveled. If the distance is the same but you have two rates, you still can’t just take the avg of the rates, you need to determine the total time traveled.

Question 2

Converging Rate Questions

Answer 2

When two objects converge at a constant rate, the sum of the distances traveled must equal the initial distance between the objects.
Ex: If two cars were 100 miles apart and traveling towards each other at a constant rate, when they meet the total distance the two cars traveled will equal 100 miles, regardless of how fast each of them traveled.

Question 3

Two Objects leave at different times

Answer 3

When two objects leave at a different time use t of 1st object = t 2nd object + delta to set-up the equations. The travel time of the object that leaves earlier should be represented by t + difference between departure times.

Question 4

Two objects: One travels faster than the other but unknown rates

Answer 4

Let the slower object’s speed be variable r and the faster object be r + difference in speeds.

Question 5

Round Trip Problems

Answer 5

When only the total time traveled is provided, let the time to a destination equal t and the time back equal (total trip - t). Set the rates * time equal to each other and solve for time.

If the velocity of half the trip distance is given (v1), the max v total cannot be more than double of v1.

Question 6

Catch-Up Rate

Answer 6

When one object follows another object at a faster rate, to solve for catch-up time, set the distances equal to each other. The object that went first will have added distance at rate * (time ahead of fast object).

If you are given the speed ratio and the time advantage, you can set the distances equal to each other and solve for T pass.

Question 7

Catch-Up and Pass

Answer 7

You can use the “net effective/relative” rate when a faster object behind a slower moving object is trying to catch-up and pass. The total distance will be the catch-up distance plus whatever pass distance the problem is asking for.

Question 8

If then rates

Answer 8

Use the original scenario variables and add/substract the new condition (i.e. speed or time) and then solve. You’ll get a quadratic.