A truck covers a distance of 550 metres in 1 minute whereas a bus covers a distance of 33 km in 45 minutes. What is the ratio of their speeds.

Answer

To find the ratio of the speeds of the truck and the bus, we need to calculate their speeds first.

### Step 1: Calculate the speed of the truck
The speed of an object is calculated using the formula:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]
For the truck:
- Distance = 550 meters
- Time = 1 minute = 60 seconds (since we need to convert minutes to seconds for consistency)

Now, substituting the values:
\[ \text{Speed of the truck} = \frac{550 \text{ meters}}{60 \text{ seconds}} = \frac{550}{60} \text{ m/s} \]
Calculating this gives:
\[ \text{Speed of the truck} = 9.17 \text{ m/s} \quad (\text{approximately}) \]

### Step 2: Calculate the speed of the bus
For the bus:
- Distance = 33 km = 33,000 meters (since 1 km = 1000 meters)
- Time = 45 minutes = 45 × 60 seconds = 2700 seconds

Now, substituting the values:
\[ \text{Speed of the bus} = \frac{33,000 \text{ meters}}{2700 \text{ seconds}} = \frac{33,000}{2700} \text{ m/s} \]
Calculating this gives:
\[ \text{Speed of the bus} = 12.22 \text{ m/s} \quad (\text{approximately}) \]

### Step 3: Find the ratio of their speeds
Now, we can find the ratio of the speeds of the truck to the bus:
\[ \text{Ratio} = \frac{\text{Speed of the truck}}{\text{Speed of the bus}} = \frac{9.17 \text{ m/s}}{12.22 \text{ m/s}} \]
Calculating this gives:
\[ \text{Ratio} \approx \frac{9.17}{12.22} \approx 0.75 \]

To express this as a ratio of whole numbers, we can multiply both sides by 100 to eliminate the decimal:
\[ \text{Ratio} \approx 75:100 \]
Simplifying this gives:
\[ \text{Ratio} = 3:4 \]

### Final Answer
The ratio of the speeds of the truck to the bus is **3:4**.

---