A car completed a journey of 400km in `12(1)/(2)` hrs. The first `(3)/(4)`th of the journey was done at 30 km/hr. Calculate the speed for the rest of the journey.

Options

A. 45km/hr
B. 25km/hr
C. 40km/hr
D. 30km/hr

Answer

To solve the problem step by step, we will follow the given information and perform the necessary calculations.

### Step 1: Understand the total journey and time taken
The total distance of the journey is 400 km, and the total time taken is \(12 \frac{1}{2}\) hours, which can be converted to an improper fraction:
\[ 12 \frac{1}{2} = \frac{25}{2} \text{ hours} \]

### Step 2: Calculate the distance covered in the first \( \frac{3}{4} \) of the journey
To find the distance covered in the first \( \frac{3}{4} \) of the journey:
\[ \text{Distance}_{\frac{3}{4}} = \frac{3}{4} \times 400 = 300 \text{ km} \]

### Step 3: Calculate the time taken for the first \( \frac{3}{4} \) of the journey
The speed for the first \( \frac{3}{4} \) of the journey is 30 km/hr. We can find the time taken to cover this distance using the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{300 \text{ km}}{30 \text{ km/hr}} = 10 \text{ hours} \]

### Step 4: Determine the time left for the remaining journey
Now, we can find the time left for the remaining \( \frac{1}{4} \) of the journey:
\[ \text{Time}_{\text{remaining}} = \text{Total time} - \text{Time for first } \frac{3}{4} = \frac{25}{2} - 10 = \frac{25}{2} - \frac{20}{2} = \frac{5}{2} \text{ hours} \]

### Step 5: Calculate the distance for the remaining journey
The remaining distance (which is \( \frac{1}{4} \) of the total journey) can be calculated as:
\[ \text{Distance}_{\frac{1}{4}} = 400 \text{ km} - 300 \text{ km} = 100 \text{ km} \]

### Step 6: Calculate the speed for the remaining journey
Now we can find the speed for the remaining distance using the formula:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{100 \text{ km}}{\frac{5}{2} \text{ hours}} = 100 \times \frac{2}{5} = 40 \text{ km/hr} \]

### Final Answer
The speed for the rest of the journey is **40 km/hr**.

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