math
posted by kanga .
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.

The trailer went 300 km in t1 hours, so its avg speed is 300/(t1)
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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