A bus moves at a speed of 84 km/hr after repairing and moves at a speed of 56 km/hr before repairing. It covers 2x distance in 8 hours after repairing. How much time (in hours) will it take to cover x distance before repairing?

Options

A. 8
B. 5
C. 6
D. 9

Answer

To solve the problem step by step, let's break it down:

### Step 1: Understand the given information
- Speed after repairing = 84 km/hr
- Speed before repairing = 56 km/hr
- Distance covered after repairing = 2x
- Time taken to cover 2x distance after repairing = 8 hours

### Step 2: Calculate the distance covered after repairing
Using the formula for distance:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]

We can find the distance covered after repairing:
\[ \text{Distance} = 84 \, \text{km/hr} \times 8 \, \text{hours} = 672 \, \text{km} \]

Since this distance is equal to 2x, we can set up the equation:
\[ 2x = 672 \]

### Step 3: Solve for x
To find x, divide both sides of the equation by 2:
\[ x = \frac{672}{2} = 336 \, \text{km} \]

### Step 4: Calculate the time taken to cover x distance before repairing
Now, we need to find out how much time it will take to cover x distance (336 km) before repairing. We use the speed before repairing:
\[ \text{Speed before repairing} = 56 \, \text{km/hr} \]

Using the formula for time:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]

We can substitute the values:
\[ \text{Time} = \frac{336 \, \text{km}}{56 \, \text{km/hr}} \]

### Step 5: Perform the division
Now, calculate the time:
\[ \text{Time} = 6 \, \text{hours} \]

### Final Answer
The bus will take **6 hours** to cover x distance before repairing.

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