A car travels from point a to point b at a speed of 60 mph and returns to point a at a speed of 80 mph. what is the average speed for the round trip?

Mathematics
1

a car travels from point a to point b at a speed of 60 mph and returns to point a at a speed of 80 mph. what is the average speed for the round trip?

2

What is the average speed for the round trip?

To find the average speed for the round trip, we can use the formula:

Average Speed = Total Distance / Total Time

Let’s assume the distance between point A and point B is “d” miles.

  1. Calculating the time taken for the first leg of the trip (from A to B):

    • Speed = 60 mph
    • Time = Distance / Speed
    • Time = d / 60

  2. Calculating the time taken for the second leg of the trip (from B to A):

    • Speed = 80 mph
    • Time = Distance / Speed
    • Time = d / 80

  3. Calculating the total distance for the round trip:

    • Total Distance = Distance from A to B + Distance from B to A
    • Total Distance = d + d
    • Total Distance = 2d

  4. Calculating the total time for the round trip:

    • Total Time = Time taken for the first leg of the trip + Time taken for the second leg of the trip
    • Total Time = d / 60 + d / 80

  5. Calculating the average speed for the round trip:

    • Average Speed = Total Distance / Total Time
    • Average Speed = 2d / (d / 60 + d / 80)

To simplify the equation, we can find a common denominator for the fractions in the denominator:

Average Speed = 2d / (d / 60 + d / 80)
Average Speed = 2d / ((4d + 3d) / (240))
Average Speed = 2d / (7d / 240)
Average Speed = (2d * 240) / 7d
Average Speed = 480 / 7
Average Speed ≈ 68.57 mph

Therefore, the average speed for the round trip is approximately 68.57 mph.