1. Two vehicles start at time t = 0 from the same point A and travel along a straight line so that at each moment t the distance between the second vehicle and A equals the square of the distance between the first vehicle and A. After t = 3 hours, the first vehicle is moving at 3 kilometers per hour and is 9 kilometers away from A. What is the speed, in kilometers per hour, of the second vehicle at t = 3 hours?
A. 9 
B. 18 
C. 27 
D. 54 
E. 81 

Solution: The answer is C
Let,
D_{1} = the distance between vehicle 1 and point A
D_{2} = the distance between vehicle 2 and point A
S_{1} = the speed of vehicle 1
S_{2} = the speed of vehicle 2
D t = time elapsed
The relationship between D_{1} and D_{2} is given by,
Since S_{1} = 3 km/hr, which is also defined as the ratio of distance and time, that is,
then, solving for D_{1} yields,
So, after 3 hours have elapsed,
and hence,
Now, to solve for S_{2} after 3 hours have elapsed, take the following ratio,