Rajiv's boat can travel along the current at the 8 km/hour and against the current at the rate 6 km/hour. Find the time taken by the boat to sail 28 km in still water.

The correct option is 4 hours.

Step 1: Understand the given information

Speed of the boat along the current (downstream speed, u) = 8 km/hour
Speed of the boat against the current (upstream speed, v) = 6 km/hour

Step 2: Find the speed of the boat in still water

The formula for the speed of a boat in still water (v_b) when downstream and upstream speeds are given is:

$v_b=\frac{u+v}{2}$

Substituting the given values into the formula:

$v_b=\frac{8+6}{2}=\frac{14}{2}=7\text{ km/hour}$

Step 3: Calculate the time taken to travel the given distance in still water

Distance to be traveled (d) = 28 km
Speed in still water (v_b) = 7 km/hour

The formula for time is:

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

Substituting the values:

$\text{Time}=\frac{28}{7}=4\text{ hours}$

Therefore, the time taken by the boat to sail 28 km in still water is 4 hours.