Final answer:
Using the relationship between distance, speed, and time, we determined that it took John 3 hours to travel to his friend's house at an average speed of 30 km/h, with the return trip at 40 km/h taking one hour less.
Step-by-step explanation:
To determine how long it took John to travel to his friend's house, we need to first understand the relationship between distance, speed, and time. The formula to calculate average speed is average speed = total distance / total time. Given that the average speed on the trip there was 30 km/h and 40 km/h on the way back, and that the return trip took one hour less, we can set up two equations to find the time it took for each leg of the journey.
Let t be the time it took for John to travel to his friend's house. Therefore, the time it took for the return trip is t - 1 hour. Since the distance to his friend's house and back is the same, we can say:
- Distance going there = 30 km/h × t
- Distance coming back = 40 km/h × (t - 1 hour)
Equating the two distances since they are the same:
30 km/h × t = 40 km/h × (t - 1 hour)
Solving the equation:
30t = 40(t-1)
30t = 40t - 40
10t = 40
t = 4 hours
However, the question asked for the time it took to travel to his friend's house, which means we need to subtract one hour from the total time:
So, the trip there took t - 1 = 4 hours - 1 hour = 3 hours.
Therefore, answer option c, 3 hours, is the correct choice.