Two trains, each $800\text{m}$ long, are running in opposite directions on parallel tracks. Their speeds are $80\text{km/h}$ and $60\text{km/h}$ respectively. Find the time taken by the slower train to pass the driver of the faster train.

Step-by-step solution:
1. Identify the distance to be covered:
Since the question asks for the time taken by the slower train to pass the driver of the faster train, the distance to be covered is equal to the length of the slower train only.

$$\text{Distance}=800\text{m}$$

2. Calculate the relative speed:
As the two trains are moving in opposite directions, their speeds will be added.

$$\text{Relative Speed}=80+60=140\text{km/h}$$

Convert the relative speed into meters per second ($\text{m/s}$):

$$\text{Relative Speed}=140\times \frac{5}{18}=\frac{700}{18}=\frac{350}{9}\text{m/s}$$

3. Calculate the time taken:

$$\text{Time}=\frac{\text{Distance}}{\text{Relative Speed}}$$

$$\text{Time}=\frac{800}{\frac{350}{9}}=\frac{800\times 9}{350}=\frac{144}{7}\approx 20.57\text{seconds}$$