A car is driven at an average speed of 30 km/hr for 15 minutes. At what speed should the car be driven, if the same distance is to be covered in 18 minutes?

Answer

To solve the problem step by step, we will follow these instructions:

### Step 1: Calculate the distance covered by the car in the first scenario.
The formula for distance is:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
Given:
- Speed = 30 km/hr
- Time = 15 minutes = \(\frac{15}{60}\) hours = \(\frac{1}{4}\) hours

Now, substituting the values into the distance formula:
\[ \text{Distance} = 30 \, \text{km/hr} \times \frac{1}{4} \, \text{hr} = \frac{30}{4} \, \text{km} = 7.5 \, \text{km} \]

### Step 2: Set up the equation for the second scenario.
We need to find the speed \(x\) at which the car should be driven to cover the same distance (7.5 km) in 18 minutes.

Convert 18 minutes into hours:
\[ 18 \, \text{minutes} = \frac{18}{60} \, \text{hours} = \frac{3}{10} \, \text{hours} \]

Using the distance formula again:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
We can set up the equation:
\[ 7.5 \, \text{km} = x \times \frac{3}{10} \, \text{hr} \]

### Step 3: Solve for \(x\).
Rearranging the equation to solve for \(x\):
\[ x = \frac{7.5 \, \text{km}}{\frac{3}{10} \, \text{hr}} = 7.5 \, \text{km} \times \frac{10}{3} \, \text{hr}^{-1} \]
Calculating the right side:
\[ x = \frac{75}{3} \, \text{km/hr} = 25 \, \text{km/hr} \]

### Conclusion:
The average speed of the car should be \(25 \, \text{km/hr}\) to cover the same distance in 18 minutes.

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