Final answer:
The average speed of the car for the entire journey is 27.43 mph.
Step-by-step explanation:
To find the average speed of the car for the entire journey, you need to calculate the total distance traveled and the total time taken. In this case, the car covered the same distance twice, so the total distance traveled is twice the initial distance. Let's assume the initial distance is D. On the first trip, the car traveled at a speed of 24 mph, so the time taken is D/24 hours. On the return trip, the car traveled at a speed of 16 mph, so the time taken is D/16 hours. The total time taken for the entire journey is (D/24) + (D/16) hours.
The total distance traveled is 2D, and the total time taken is (D/24) + (D/16) hours. To find the average speed, divide the total distance by the total time: (2D)/((D/24) + (D/16)). Simplifying this expression, we get:
Average Speed = (2D)/((D/24) + (D/16)) = (48D)/(D + 3D/4) = (48D)/(7D/4) = (48/7) x 4 mph = 27.43mm