Sets for an overlapping sets problem it is best to use a double set matrix to organize the information and solve. Fill in the information in the order in which it is given

80/3
---
T	2	3	5
D	80	80	160

This results in an average speed of 32 miles per hour.

It does not matter that we chose a random distance of 80; we would able to solve using any distance or even using a variable x as the distance. The times would adjust accordingly based on the distance we used and the same average speed of 32 would result.

INSUFFICIENT: If all we know is the distance from Riverdale to Smallville, we will be able to find the time traveled on the way there but we will have no indication of how fast the car traveled on the way back and therefore no way of knowing what the average overall speed was.

The correct answer is A.

20.
The average speed is defined to be the total distance of the trip, divided by the total time of the trip. The question stem tells us the distance from New York to Boston is 250 miles, so we can rephrase the question as "How long did it take Bill to drive from New York to Boston?"
SUFFICIENT: Statement (1) tells us it took Bill 5 hours to drive from New York to Boston, answering the rephrased question. In fact, his average rate of speed equals 250/5 = 50 miles per hour.
INSUFFICIENT: Statement (2) tells us that at the midpoint of the trip Bill was going exactly 50 miles per hour, but we can't figure out how long the trip took from this information. Bill may have traveled at a constant rate of 50 mph throughout the whole trip, but he might also have been going faster or slower at different times.
The correct answer is A.

21.
We can attack this problem by first setting up a rate chart, identifying what we already know, and using variables for any unknown values:

	Train A	Train B
Rate	100 mph	r
Time	2 - t	t
Distance	d	d

The chart yields two equations:

We also know that when the trains pass each other (going in opposite directions), Train A has been traveling for 1 hour and Train B has been traveling for 10 minutes or 1/6 of an hour.

This means that Train A has traveled 100 miles and Train B has traveled miles.

Thus, the total distance from New York to Boston can be expressed using the equation, .

We now have three equations and three variables: 

Setting equation (A) and equation (B) to be equal, we can solve for t, as follows:

Then we can set equation (B) and equation (C) to be equal, substitute for t, and solve for r as follows:

Thus, the rate, r, of Train B is either 300 mph or 200 mph. Using this information we can chart out the two possible scenarios.