Final answer:
To find the average speed for the entire journey, we must first calculate the distance between the towns using the given average speeds for each leg of the trip and the total time of 10 hours. Once the distance is known, we double it to account for the round trip and divide by the total time to obtain the overall average speed.
Step-by-step explanation:
The question asks to calculate the average speed of a car traveling between two towns and back when the average speeds in each direction and the total time taken are known.
To solve this, we can let the distance between town p and q be d kilometers. The time taken to travel from p to q at an average speed of 75 km/h is d/75 hours, and the time taken to return from q to p at an average speed of 65 km/h is d/65 hours. The total time for both journeys is 10 hours, so we have the equation d/75 + d/65 = 10. Solving for d gives us the distance between the towns, which can be used to find the overall average speed for the entire trip.
The average speed for the trip is the total distance traveled (which is 2d because the car travels the distance twice) divided by the total time taken for the trip. So, the average speed = 2d/10 hours.