To determine the average speed for the trip from Townsend to Smallville and back again, we need to know the average speed in each direction. Because the distance in each direction is the same, if we have the average speed in each direction we will be able to find the average speed of the entire trip by taking the total distance and dividing it by the total time.
(1) SUFFICIENT: This allows us to figure out the average speed for the return trip. If the return time was 3/2 the outgoing time, the return speed must have been 2/3 that of the outgoing. Whenever the distance is fixed, the ratio of the times will be the inverse of the ratio of the speeds.
We can see this by looking at an example. Let's say the distance between the two towns was 80 miles.
Going Returning
R 40
T
D 80 80
We can calculate the "going" time as 2 hours. Since, the return trip took 50% longer, the "returning time" is 3 hours. Thus, the average rate for the return trip is Distance/Time or 80/3 miles per hour.
Going Returning
R 40 80/3
T 2 3
D 80 80
We can use this table to calculate the average speed for the entire trip: take the total distance, 160, and divide by the total time, 5.
Going Returning TOTAL
R 40 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.
(2) 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.
Predeep's explanation is much easier to understand
