A body runs 20km in 2.5 hours. How long will he take to run 32 km at double the previous speed?

Options

A. 2 hours
B. `2(1)/(2)` hours
C. `4(1)/(2)` hours
D. 5 hours

Answer

To solve the problem step by step, we will follow the speed, distance, and time relationships.

### Step 1: Calculate the initial speed
We know that speed is calculated using the formula:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]
From the question, the body runs 20 km in 2.5 hours.

Substituting the values:
\[ \text{Speed} = \frac{20 \text{ km}}{2.5 \text{ hours}} = 8 \text{ km/h} \]

### Step 2: Determine the new speed
The question states that the body will run at double the previous speed. Therefore, we calculate the new speed:
\[ \text{New Speed} = 2 \times 8 \text{ km/h} = 16 \text{ km/h} \]

### Step 3: Calculate the time taken to run 32 km at the new speed
Now, we need to find out how long it will take to run 32 km at the new speed of 16 km/h. We will use the formula for time:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]
Substituting the values:
\[ \text{Time} = \frac{32 \text{ km}}{16 \text{ km/h}} = 2 \text{ hours} \]

### Final Answer
The body will take **2 hours** to run 32 km at double the previous speed.

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