A scooter runs at a speed of 49 km/hr after repairing and runs at 42km/hr before repairing. It covers a certain distance in 7 hours after repairing. How much time will it take to cover twice of the distance before repairing?

Options

A. 8 hours 10 minutes
B. 12 hours 20 minutes
C. 16 hours 20 minutes
D. 18 hours 30 minutes

Answer

To solve the problem step by step, we will follow the information given in the question and apply the relevant formulas.

### Step 1: Calculate the distance covered after repairing
The formula for distance is:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
After repairing, the speed of the scooter is 49 km/hr and the time taken is 7 hours.

So, we calculate the distance:
\[ \text{Distance} = 49 \, \text{km/hr} \times 7 \, \text{hr} = 343 \, \text{km} \]

### Step 2: Determine the distance to be covered before repairing
The problem states that we need to find the time taken to cover twice the distance before repairing. Therefore, the distance to be covered before repairing is:
\[ D' = 2 \times 343 \, \text{km} = 686 \, \text{km} \]

### Step 3: Calculate the time taken to cover the distance before repairing
Before repairing, the speed of the scooter is 42 km/hr. We will use the formula for time:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]
Substituting the values we have:
\[ \text{Time} = \frac{686 \, \text{km}}{42 \, \text{km/hr}} \]

### Step 4: Simplify the calculation
Now, we simplify the calculation:
\[ \text{Time} = \frac{686}{42} \]
Calculating this gives:
\[ \text{Time} = 16.3333 \, \text{hours} \quad \text{(which is } 16 \frac{1}{3} \text{ hours)} \]

### Step 5: Convert the fractional time into hours and minutes
To convert \( \frac{1}{3} \) of an hour into minutes:
\[ \frac{1}{3} \text{ hour} = \frac{1}{3} \times 60 \text{ minutes} = 20 \text{ minutes} \]
Thus, the total time taken is:
\[ 16 \text{ hours and } 20 \text{ minutes} \]

### Final Answer
The time taken to cover twice the distance before repairing is **16 hours and 20 minutes**.

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