A man travelled a distance of 80 km in 7 hrs partly on foot at the rate of 8 km per hour and partly on bicycle at 16km per hour. The distance travelled on the foot is

Options

A. 32km
B. 48km
C. 36km
D. 44km

Answer

To solve the problem step by step, we will break down the information given and use the relationships between distance, speed, and time.

### Step 1: Define Variables
Let:
- \( x \) = distance traveled on the bicycle (in km)
- \( 80 - x \) = distance traveled on foot (in km)

### Step 2: Write the Equations for Time
We know that:
- Speed on the bicycle = 16 km/h
- Speed on foot = 8 km/h

The time taken to travel by bicycle can be expressed as:
\[ \text{Time}_{\text{bicycle}} = \frac{x}{16} \]

The time taken to travel on foot can be expressed as:
\[ \text{Time}_{\text{foot}} = \frac{80 - x}{8} \]

### Step 3: Set Up the Total Time Equation
The total time for the journey is given as 7 hours. Therefore, we can write the equation:
\[ \frac{x}{16} + \frac{80 - x}{8} = 7 \]

### Step 4: Solve the Equation
To solve the equation, we first find a common denominator. The least common multiple of 16 and 8 is 16. We can rewrite the equation as:
\[ \frac{x}{16} + \frac{2(80 - x)}{16} = 7 \]

This simplifies to:
\[ \frac{x + 160 - 2x}{16} = 7 \]
\[ \frac{160 - x}{16} = 7 \]

Now, multiply both sides by 16:
\[ 160 - x = 112 \]

Rearranging gives:
\[ x = 160 - 112 \]
\[ x = 48 \]

### Step 5: Find the Distance Traveled on Foot
Now that we have \( x \), we can find the distance traveled on foot:
\[ \text{Distance on foot} = 80 - x = 80 - 48 = 32 \text{ km} \]

### Final Answer
The distance traveled on foot is **32 km**.

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