The speed of a boat downstream is 15 km/hr and the speed of the stream is 1.5 km/hr. The speed of the boat upstream is -----

Options

A. 13.5 km/hr
B. 16.5 km/hr
C. 12 km/hr
D. 8.25 km/hr

Answer

To find the speed of the boat upstream, we can follow these steps:

### Step 1: Understand the given information
- The speed of the boat downstream (V_d) = 15 km/hr
- The speed of the stream (Y) = 1.5 km/hr

### Step 2: Use the formula for downstream speed
The downstream speed of the boat can be expressed as:
\[ V_d = X + Y \]
Where:
- \( X \) = speed of the boat in still water (unknown)
- \( Y \) = speed of the stream

### Step 3: Substitute the known values into the equation
We can substitute the known values into the equation:
\[ 15 = X + 1.5 \]

### Step 4: Solve for X
To find \( X \), we rearrange the equation:
\[ X = 15 - 1.5 \]
\[ X = 13.5 \text{ km/hr} \]

### Step 5: Use the formula for upstream speed
The upstream speed of the boat can be expressed as:
\[ V_u = X - Y \]
Where:
- \( V_u \) = speed of the boat upstream (unknown)

### Step 6: Substitute the known values into the upstream equation
Now we can substitute the values of \( X \) and \( Y \):
\[ V_u = 13.5 - 1.5 \]

### Step 7: Solve for V_u
Calculating the upstream speed:
\[ V_u = 12 \text{ km/hr} \]

### Final Answer
The speed of the boat upstream is **12 km/hr**.

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