Sabrina travelled 8 km/hr on foot and 13 km/hr on cycle. She travelled a distance of 84 km in 8 hours. for how many hours did she cycle?

Options

A. 4
B. 5
C. 3
D. 2

Answer

To solve the problem, we need to determine how many hours Sabrina cycled given her speeds on foot and on a cycle, as well as the total distance and time traveled.

### Step-by-Step Solution:

1. **Identify the Variables:**
- Let \( x \) be the distance Sabrina traveled on foot (in km).
- Therefore, the distance she traveled on the cycle is \( 84 - x \) km (since the total distance is 84 km).

2. **Write the Speeds:**
- Speed on foot = 8 km/hr
- Speed on cycle = 13 km/hr

3. **Set Up the Time Equation:**
- Time taken to walk \( = \frac{x}{8} \) hours
- Time taken to cycle \( = \frac{84 - x}{13} \) hours
- The total time for the journey is 8 hours.

Thus, we can write the equation:
\[ \frac{x}{8} + \frac{84 - x}{13} = 8 \]

4. **Eliminate Fractions:**
- To eliminate the fractions, find a common denominator. The least common multiple of 8 and 13 is 104.
- Multiply the entire equation by 104:
\[ 104 \left(\frac{x}{8}\right) + 104 \left(\frac{84 - x}{13}\right) = 104 \cdot 8 \]
This simplifies to:
\[ 13x + 8(84 - x) = 832 \]

5. **Distribute and Combine Like Terms:**
- Distributing the 8:
\[ 13x + 672 - 8x = 832 \]
- Combine like terms:
\[ 5x + 672 = 832 \]

6. **Isolate \( x \):**
- Subtract 672 from both sides:
\[ 5x = 832 - 672 \]
\[ 5x = 160 \]
- Divide by 5:
\[ x = \frac{160}{5} = 32 \]

7. **Calculate the Distance Covered by Cycle:**
- Distance covered by cycle \( = 84 - x = 84 - 32 = 52 \) km.

8. **Calculate the Time Taken to Cycle:**
- Time taken to cycle \( = \frac{52}{13} = 4 \) hours.

### Final Answer:
Sabrina cycled for **4 hours**.