A boat covers 144 km in downstream and 224 km in upstream in 8 hours and 16 hours respectively. Find the time taken by boat to cover 128 km in still water.

The correct answer is Option 2: 8 hours.

Step-by-step Explanation:

Step 1: Calculate the Downstream Speed (D)
Downstream speed is the speed of the boat traveling with the direction of the water current.
Distance covered downstream = 144 km
Time taken downstream = 8 hours

$\text{Downstream Speed (D)}=\frac{\text{Distance covered downstream}}{\text{Time taken downstream}}$

$\text{D}=\frac{144}{8}=18\text{km/h}$

Step 2: Calculate the Upstream Speed (U)
Upstream speed is the speed of the boat traveling against the direction of the water current.
Distance covered upstream = 224 km
Time taken upstream = 16 hours

$\text{Upstream Speed (U)}=\frac{\text{Distance covered upstream}}{\text{Time taken upstream}}$

$\text{U}=\frac{224}{16}=14\text{km/h}$

Step 3: Calculate the Speed of the Boat in Still Water (B)
The formula for the speed of the boat in still water is the average of downstream speed and upstream speed:

$\text{Speed of boat in still water (B)}=\frac{\text{D}+\text{U}}{2}$

$\text{B}=\frac{18+14}{2}=\frac{32}{2}=16\text{km/h}$

Step 4: Find the Time Taken to Cover 128 km in Still Water
Target distance = 128 km
Speed in still water = 16 km/h

$\text{Time taken}=\frac{\text{Distance}}{\text{Speed in still water}}$

$\text{Time taken}=\frac{128}{16}=8\text{hours}$

Thus, the boat takes 8 hours to cover 128 km in still water.