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Answer :
Final answer:
The average speed for the journey is calculated by dividing the total distance of the round trip by the total time taken. The journey's constant distance is symbolized by 'd', and after solving for the average speed, the result is approximately 34.3 km/hr.
Explanation:
To find the average speed of a person who travels a constant distance from A to B at 40 km/hr and then returns at 30 km/hr, we need to consider the total distance traveled and the total time taken for the round trip. Average speed is defined by the total distance divided by the total time.
First, we let the constant distance be 'd' km. The time taken to travel from A to B at 40 km/hr is t1 = d / 40 hr. The time to return from B to A at 30 km/hr is t2 = d / 30 hr. The total distance for the round trip is 2d km.
The total time for the trip is t1 + t2 = d/40 + d/30. By finding a common denominator, we can add these two expressions to get the total time as (3d + 4d) / 120 = 7d / 120 hr. Thus, the average speed for the entire trip is the total distance divided by the total time, which is (2d) / (7d/120) = 240/7 km/hr, which is approximately 34.3 km/hr.
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