Question:

A car covers one-quarter of the distance to the enxt town at 40 km/h, another quarter at 50 km/h?

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and the rest at 90 km/h. Find the car's average speed for the entire distance.

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  1. The average of the 4 speeds

    (40 + 50 + 90 + 90) / 4

    270 / 4 = 67.5 km/h

    Edit: JonDihon's weighted average, is probably a better answer.


  2. This is a trick question. The car goes at the different speeds for different amount of times. The average speed is a weighted average depending on what fraction of the time it traveled at the different speeds.

    It's easier just to divide the distance by the total time.

    d = 40t_1 + 50t_2 + 90t_3

    40t_1 = d/4

    t_1 = d/160

    50t_2 = d/4

    t_2 = d/200

    90t_3 = d/2

    t_3 = d/180

    average speed = d/(t_1 + t_2 + t_3)

    average speed = d/(d/160 + d/200 + d/180) = 1/(1/160 + 1/200 + 1/180)

    = 20d/(d/8 + d/10 + d/9)

    = 20/(1/8 + 1/10 + 1/9)

    = 20/(45/360 + 36/360 + 40/360)

    = 20/(121/360)

    =59.5 km/h

    If the distance is 180 km it goes 45 km at 40 km/h in 1.125 hr.

    It goes 45 km at 50 km/h in 0.9 hr.

    It goes 90 km at 90 km/h in 1 hr.

    It travels the 180 km in 3.025 hr.

    180/3.025 = 59.5 km/h

    The weighted average of the 3 speeds

    (40*1.125 + 50*0.9 + 90*1)/3.025 = 59.5 km/h.

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