Final answer:
The distance between points A and B is 0.9 km. Therefore, the total distance traveled during the round trip is 1.8 km.
Step-by-step explanation:
To find the distance traveled by the man, we will use the concept of speed, distance, and time. The man travels from A to B at 4 km/h and returns from B to A at 6 km/h. The total journey takes 45 minutes, which is 0.75 hours (since 45 minutes is ⅔ of an hour).
Let's let the distance between A and B be D kilometers. Using the formula speed = distance / time, the time taken to travel from A to B is D / 4 hours, and the time taken to travel back from B to A is D / 6 hours.
To find D, we set up the equation:
D / 4 + D / 6 = 0.75
By finding a common denominator and solving for D, we have:
3D + 2D = 6 × 0.75
5D = 4.5
D = 0.9 km
Therefore, the total distance traveled is D there and back, or 1.8 km.