A boat covers 143 km upstream in 13 hourse and the same distance downstream in 11 hours. What is the speed (in km /hr ) of the boat in still water ?

Options

A. 10
B. 12
C. 14
D. 8

Answer

To find the speed of the boat in still water, we will follow these steps:

### Step 1: Calculate the upstream speed
The speed of the boat upstream (Uss) can be calculated using the formula:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]
Here, the distance is 143 km and the time taken is 13 hours.

So,
\[ \text{Uss} = \frac{143 \text{ km}}{13 \text{ hours}} \]
Calculating this gives:
\[ \text{Uss} = 11 \text{ km/hr} \]

### Step 2: Calculate the downstream speed
Similarly, the speed of the boat downstream (Dss) can be calculated using the same formula:
\[ \text{Dss} = \frac{143 \text{ km}}{11 \text{ hours}} \]
Calculating this gives:
\[ \text{Dss} = 13 \text{ km/hr} \]

### Step 3: Calculate the speed of the boat in still water
The speed of the boat in still water (S) can be found using the formula:
\[ S = \frac{\text{Uss} + \text{Dss}}{2} \]
Substituting the values we calculated:
\[ S = \frac{11 \text{ km/hr} + 13 \text{ km/hr}}{2} \]
Calculating this gives:
\[ S = \frac{24 \text{ km/hr}}{2} = 12 \text{ km/hr} \]

### Final Answer
The speed of the boat in still water is **12 km/hr**.

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