Final answer:
The average speed of a car for a round trip is not the arithmetic mean of the two speeds but is calculated based on the total distance divided by the total time travelled. Given the distances and speeds in the question, the average speed for the trip is calculated to be 19.2 mph,
with the closest answer being 20 mph.
Step-by-step explanation:
The average speed for a round trip is not simply the arithmetic mean of the two speeds, because the car spends more time traveling at the slower speed. To calculate the average speed, we need to use the formula:
Average Speed = Total Distance / Total Time
Given that the car covered the same distance at 24 mph and then at 16 mph, we assume this distance is 'd' (which cancels out in the calculation). Let's call time taken to travel at 24 mph t1 and at 16 mph t2. The total distance covered in the round trip is then 2d.
Time taken to travel a distance 'd' at 24 mph (t1) = d/24.
Time taken to travel a distance 'd' at 16 mph (t2) = d/16.
Total Time (t1 + t2) = d/24 + d/16.
To calculate the average speed:
Average Speed = 2d / (d/24 + d/16)
Average Speed = 2d / (2d/48 + 3d/48)
Average Speed = 2d / (5d/48)
Average Speed = 2 * 48 / 5
Average Speed = 96 / 5
Average Speed = 19.2 mph
The answer closest to this value is (b) 20 mph.