A man covers a certain distance in 40 minutes at a speed of 45 kmph. If he wants to cover the distance in 30 minutes, how much speed will be increase ?

Options

A. 10 km/hr
B. 12 km/hr
C. 15 km/hr
D. 25 km/hr

Answer

To solve the problem step by step, we need to find out how much speed needs to be increased for the man to cover the same distance in a shorter time. Here’s how we can do it:

### Step 1: Identify the given data
- Speed (S1) = 45 km/h
- Time (T1) = 40 minutes

### Step 2: Convert time from minutes to hours
To work with speed in km/h, we need to convert the time from minutes to hours.
- T1 in hours = 40 minutes ÷ 60 = 2/3 hours

### Step 3: Calculate the distance covered
Using the formula for distance:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
We can calculate the distance (D):
\[ D = 45 \, \text{km/h} \times \frac{2}{3} \, \text{h} = 30 \, \text{km} \]

### Step 4: Determine the new time
The man wants to cover the same distance in 30 minutes.
- T2 = 30 minutes = 30 ÷ 60 = 1/2 hours

### Step 5: Calculate the required speed to cover the distance in the new time
Using the distance calculated earlier, we can find the new speed (S2) required:
\[ S2 = \frac{D}{T2} = \frac{30 \, \text{km}}{1/2 \, \text{h}} = 30 \times 2 = 60 \, \text{km/h} \]

### Step 6: Calculate the increase in speed
Now we find out how much speed needs to be increased:
\[ \text{Increase in speed} = S2 - S1 = 60 \, \text{km/h} - 45 \, \text{km/h} = 15 \, \text{km/h} \]

### Final Answer
The speed needs to be increased by **15 km/h**.

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