A car covers a distance of `2 km` in `2.5` minutes. If it covers half of the distance with speed `40km//hr`, the rest distance it shall cover with a speed of `:`

Options

A. `56km//hr`
B. `60km//hr`
C. `48km//hr`
D. `50km//hr`

Explanation

To solve the problem step by step, we will first summarize the given information and then calculate the required speed for the remaining distance.

### Step 1: Understand the total distance and time
The total distance covered by the car is 2 km, and the total time taken is 2.5 minutes.

### Step 2: Convert the total time into hours
Since speed is usually expressed in kilometers per hour (km/hr), we need to convert the time from minutes to hours.
\[ \text{Total time in hours} = \frac{2.5 \text{ minutes}}{60} = \frac{2.5}{60} \text{ hours} = \frac{1}{24} \text{ hours} \]

### Step 3: Calculate the distance covered at the first speed
The car covers half of the total distance (1 km) at a speed of 40 km/hr. We can calculate the time taken to cover this distance.
\[ \text{Distance} = 1 \text{ km}, \quad \text{Speed} = 40 \text{ km/hr} \]
Using the formula \( \text{Time} = \frac{\text{Distance}}{\text{Speed}} \):
\[ \text{Time taken to cover 1 km} = \frac{1 \text{ km}}{40 \text{ km/hr}} = \frac{1}{40} \text{ hours} \]

### Step 4: Convert the time taken into minutes
To convert the time taken into minutes:
\[ \text{Time in minutes} = \frac{1}{40} \text{ hours} \times 60 \text{ minutes/hour} = \frac{60}{40} = 1.5 \text{ minutes} \]

### Step 5: Calculate the remaining time
Now, we can find out how much time is left after covering the first half of the distance:
\[ \text{Remaining time} = \text{Total time} - \text{Time for first half} = 2.5 \text{ minutes} - 1.5 \text{ minutes} = 1 \text{ minute} \]

### Step 6: Calculate the speed for the second half of the distance
The remaining distance to cover is also 1 km. We can calculate the speed required to cover this distance in the remaining time.
\[ \text{Distance} = 1 \text{ km}, \quad \text{Time} = 1 \text{ minute} = \frac{1}{60} \text{ hours} \]
Using the formula \( \text{Speed} = \frac{\text{Distance}}{\text{Time}} \):
\[ \text{Speed} = \frac{1 \text{ km}}{\frac{1}{60} \text{ hours}} = 1 \text{ km} \times 60 = 60 \text{ km/hr} \]

### Final Answer
The speed at which the car shall cover the remaining distance is **60 km/hr**.

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