A farmer travelled a distance of 61 km in 9 hrs . He travelled partly on foot at the rate of 4 km/hr and partly on bicycle at the rate of 9 km/hr . The distance travelled on foot is

Options

A. 17 km
B. 16 km
C. 15 km
D. 14 km

Explanation

To solve the problem step by step, we will use the information given about the distances traveled by the farmer on foot and by bicycle, along with their respective speeds.

### Step 1: Define the variables
Let:
- \( x \) = distance traveled on foot (in km)
- \( y \) = distance traveled on bicycle (in km)

### Step 2: Set up the equations
From the problem, we know:
1. The total distance traveled is 61 km:
\[ x + y = 61 \]
2. The total time taken is 9 hours. The time taken to travel on foot and on bicycle can be expressed as:
\[ \frac{x}{4} + \frac{y}{9} = 9 \]

### Step 3: Substitute \( y \) in the time equation
From the first equation, we can express \( y \) in terms of \( x \):
\[ y = 61 - x \]
Now, substitute \( y \) into the time equation:
\[ \frac{x}{4} + \frac{61 - x}{9} = 9 \]

### Step 4: Clear the fractions
To eliminate the fractions, we can multiply the entire equation by the least common multiple (LCM) of the denominators (which is 36):
\[ 36 \left(\frac{x}{4}\right) + 36 \left(\frac{61 - x}{9}\right) = 36 \cdot 9 \]
This simplifies to:
\[ 9x + 4(61 - x) = 324 \]

### Step 5: Simplify the equation
Distributing the 4:
\[ 9x + 244 - 4x = 324 \]
Combine like terms:
\[ 5x + 244 = 324 \]

### Step 6: Solve for \( x \)
Subtract 244 from both sides:
\[ 5x = 324 - 244 \]
\[ 5x = 80 \]
Now, divide by 5:
\[ x = \frac{80}{5} = 16 \]

### Step 7: Find \( y \)
Now, substitute \( x \) back into the equation for \( y \):
\[ y = 61 - x = 61 - 16 = 45 \]

### Conclusion
The distance traveled on foot is:
\[ \boxed{16 \text{ km}} \]