To find the average speed for the entire trip, we can use the formula:
Average speed = Total distance / Total time
Let’s assume the distance from your starting point to the city is D.
When you drive to the city at an average speed of 40 km/h, the time taken for this part of the trip is given by:
Time taken = Distance / Speed = D / 40 km/h
Similarly, when you return at an average speed of 60 km/h, the time taken for this part of the trip is:
Time taken = Distance / Speed = D / 60 km/h
Now, let’s calculate the total distance for the round trip:
Total distance = Distance to the city + Distance from the city back to the starting point
= D + D
= 2D
To calculate the total time for the round trip, we add the time taken for the trip to the city and the time taken for the return trip:
Total time = Time taken for the trip to the city + Time taken for the return trip
= D / 40 km/h + D / 60 km/h
Now, let’s substitute the values into the formula for average speed:
Average speed = Total distance / Total time
= 2D / (D / 40 km/h + D / 60 km/h)
To simplify the equation, we find a common denominator:
Average speed = 2D / [(3D + 2D)/(40 km/h * 60 km/h)]
= 2D / (5D / (40 km/h * 60 km/h))
= 2D * (40 km/h * 60 km/h) / 5D
Simplifying further:
Average speed = (2 * 40 * 60) / 5 km/h
= 96 km/h
Therefore, the average speed for the entire trip is 96 km/h, not 50 km/h, due to the uneven distribution of time during the trip.
I hope this helps.