A train covers a distance of 51 km in 45 minutes .How long will take to cover 221 km?

Answer

To solve the problem step by step, we will use the unitary method.

### Step 1: Find the time taken to cover 1 km.
The train covers 51 km in 45 minutes.

To find the time taken to cover 1 km, we divide the total time by the distance:
\[ \text{Time for 1 km} = \frac{45 \text{ minutes}}{51 \text{ km}} = \frac{45}{51} \text{ minutes/km} \]

### Step 2: Calculate the time taken to cover 221 km.
Now that we know the time taken to cover 1 km, we can find the time taken to cover 221 km by multiplying the time for 1 km by 221:
\[ \text{Time for 221 km} = \frac{45}{51} \times 221 \]

### Step 3: Simplify the calculation.
To simplify the calculation:
\[ \text{Time for 221 km} = \frac{45 \times 221}{51} \]
Calculating \(45 \times 221\):
\[ 45 \times 221 = 9945 \]
Now, divide by 51:
\[ \text{Time for 221 km} = \frac{9945}{51} = 195 \text{ minutes} \]

### Step 4: Convert minutes into hours and minutes.
Now we need to convert 195 minutes into hours and minutes.
1 hour = 60 minutes, so:
\[ 195 \text{ minutes} = 3 \text{ hours} \text{ and } 15 \text{ minutes} \text{ (since } 195 - 180 = 15\text{)} \]

### Final Answer:
The train will take **3 hours and 15 minutes** to cover 221 km.

---