The ratio of speed of 3 cars are $3:4:6$. What is the ratio of time taken by these cars to cover the same distance?

We know that $\text{Distance}=\text{Speed}\times \text{Time}$.
When the distance is constant, speed and time are inversely proportional to each other ($T\propto \frac{1}{S}$).

Given the ratio of speeds of 3 cars:

$$S_1:S_2:S_3=3:4:6$$

Therefore, the ratio of time taken will be:

$$T_1:T_2:T_3=\frac{1}{3}:\frac{1}{4}:\frac{1}{6}$$

To convert this into a simple integer ratio, multiply each term by the LCM of denominators (3, 4, and 6), which is 12:

$$T_1:T_2:T_3=\left(\frac{1}{3}\times 12\right):\left(\frac{1}{4}\times 12\right):\left(\frac{1}{6}\times 12\right)$$

$$T_1:T_2:T_3=4:3:2$$