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29 September, 17:13

A person travels by car from one city to another with different constant speeds between pairs of cities. She drives for 30.0 min at 80.0 km/h, 45.0 min at 40 km/h and 12.0 min at 100 km/h, and spends 15.0 min eating lunch and buying gas. Determine the average sped for the trip. Determine the difference between the intial citties along the route.

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  1. 29 September, 19:46
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    Average speed of the trip = 52.9 km/h

    Distance between initial pairs of cities (start to end) = 70.0 km

    Explanation:

    Since distance = speed * time

    If she drives 30.0 min at 80.0 km/h

    Distance covered = (30/60) * 80 = 40.0 km

    Again she drives 45.0 min at 40 km/h

    Distance covered = (45/60) * 40 = 30.0 km

    Again she drives 12.0 min at 100 km/h

    Distance covered = (12/60) * 100 = 20.0 km

    Total distance covered = 40.0 + 30.0 + 20.0

    = 90.0 km

    Total time spent = 30.0 + 45.0 + 12.0 + 15.0

    = 102 min

    Average speed for the trip = Total distance covered/total time spent

    = 90 / (102/60)

    = 52.9 km/h

    Distance between initial cities will be between the start of one city to the end of another

    Between the first pairs = 40.0 + 30.0 = 70.0 km

    Between the second pairs = 30.0 + 20.0 = 50.0 km
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