I would think of this in terms of distance / time graph
As we know equations of straight line Y=Mx+C
M = Grad = Speed. C = Y intercept (x=0)
For car 1
Y = 90x + 0
For car 2
Y = 100x + C
0 = 100(10/60)+C
C= -100(10/60) = -16.666
Y=100x – 16.666
To find when they meet.
90x + 0 = 100x – 16.666
16.666/10 = x
x = 1.66666 = 1hr 40mins = 15:40
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Dist would be 1.666 * 90 = 150km
chk 1.666 * 100 - 16.666 = 150
Hope that helps
Andy D.