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,

D1 = the distance between vehicle 1 and point A

D2 = the distance between vehicle 2 and point A

S1 = the speed of vehicle 1

S2 = the speed of vehicle 2

D t = time elapsed

The relationship between D1 and D2 is given by,

Since S1 = 3 km/hr, which is also defined as the ratio of distance and time, that is,

then, solving for D1 yields,

So, after 3 hours have elapsed,

and hence,

Now, to solve for S2 after 3 hours have elapsed, take the following ratio,