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 step by step, we can follow these instructions:

### Step 1: Define Variables
Let the time Sabrina spent cycling be \( t \) hours. Therefore, the time she spent walking will be \( 8 - t \) hours (since the total time is 8 hours).

**Hint:** Define variables for the unknowns in the problem to simplify calculations.

### Step 2: Write the Distance Equations
Using the formula for distance (Distance = Speed × Time), we can write the distances for both walking and cycling:
- Distance walked = Speed on foot × Time walking = \( 8 \text{ km/hr} \times (8 - t) \)
- Distance cycled = Speed on cycle × Time cycling = \( 13 \text{ km/hr} \times t \)

**Hint:** Use the distance formula to express distances in terms of the defined variables.

### Step 3: Set Up the Total Distance Equation
The total distance traveled is the sum of the distances walked and cycled, which equals 84 km:
\[ 8(8 - t) + 13t = 84 \]

**Hint:** Combine the distances into a single equation that represents the total distance.

### Step 4: Expand and Simplify the Equation
Expanding the left side:
\[ 64 - 8t + 13t = 84 \]
Combine like terms:
\[ 64 + 5t = 84 \]

**Hint:** Make sure to combine like terms carefully to avoid mistakes.

### Step 5: Solve for \( t \)
Subtract 64 from both sides:
\[ 5t = 84 - 64 \]
\[ 5t = 20 \]
Now, divide both sides by 5:
\[ t = \frac{20}{5} = 4 \]

**Hint:** Isolate the variable to find its value.

### Step 6: Conclusion
Sabrina spent \( t = 4 \) hours cycling.

**Final Answer:** The time she cycled is **4 hours**.

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