math

Two towns P and Q are 400 km apart. A bus left for P and Q. It stopped at Q for one hour and then started the return to P. one hour after the departure of the bus from P, a trail also heading for Q left P. the trailer met the returning bus ¾ of the way from P to Q. they met t hours after the departure of the bus from P.

(a) Express the average speed of the trailer in terms of t

(b) Find the ratio of the speed of the bus so that of the trailer.

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  1. The trailer went 300 km in t-1 hours, so its avg speed is 300/(t-1)

    Let the bus's speed be x, and the trailer's speed be y.

    The bus went 500 km.
    Its time spent on the trip before meeting the trailer was t = 400/x + 1 + 100/x = 1 + 500/x hours

    The trailer was on the road for 300/y hours

    so, 300/y = 500/x
    (b) x/y = 5/3

    check:
    x=50, y=30

    400/50 + 1 + 100/50 = 11 hrs
    300/30 = 10, or 1 hours less

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