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

Answer

To solve the problem step by step, we will use the concept of relative speeds and the relationship between distance, speed, and time.

### Step 1: Define Variables
Let:
- \( d_f \) = distance travelled on foot (in km)
- \( d_b \) = distance travelled on bicycle (in km)

From the problem, we know:
- Total distance \( d_f + d_b = 61 \) km
- Total time \( \frac{d_f}{4} + \frac{d_b}{9} = 9 \) hours

### Step 2: Express \( d_b \) in terms of \( d_f \)
From the first equation, we can express \( d_b \):
\[ d_b = 61 - d_f \]

### Step 3: Substitute \( d_b \) in the time equation
Now, substitute \( d_b \) in the time equation:
\[ \frac{d_f}{4} + \frac{61 - d_f}{9} = 9 \]

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

### Step 5: Expand and simplify
Expanding the equation:
\[ 9d_f + 244 - 4d_f = 324 \]
Combine like terms:
\[ 5d_f + 244 = 324 \]

### Step 6: Solve for \( d_f \)
Subtract 244 from both sides:
\[ 5d_f = 80 \]
Now divide by 5:
\[ d_f = 16 \]

### Conclusion
The distance travelled on foot is \( \boxed{16} \) km.

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