physical science

A person takes a trip, driving with a constant speed 85.6 km/h except for a 22.6 minute rest stop.
If the person's average speed is 61.6 km/h, how far is the trip? Answer in units of km.

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  1. Let T be the total time (in hours) and X be the distance (in km). 22.6 minutes is 0.3767 hours. You can write two equations in the two unknowns:
    X = 61.6 T (using the average speed)
    and
    X = 85.6 (T-.03767)
    (using the time spent actually driving)
    This means that
    61.6 T = 85.6 T - 32.24
    24.0 T = 32.24
    T = 1.343 h
    Now solve for X
    X = ?

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  2. 22.6 minutes is 22.6/60 hours = 0.3737 hours

    If for simplicity we take the rest stop at the start the total journey time is (0.3767 + t)
    where t is the driving time.

    If d is the distance travelled then speed =
    d/t=85.6 km/h

    However the average speed is from time zero, thus speed from time zero

    is d/(t+0.3767)=61.6 km/h

    Next step is to rearrange
    d/t=85.6 km/h
    with t as the subject and substitute in

    d/(t+0.3767)=61.6 km/h

    and solve for d

    Hope this is OK.

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