A truck covers a distance of 550 metre in one minute where as a bus covers a distance of 33km in `(3)/(4)` hours. Then the ratio of their speeds is:

Options

A. `1:3`
B. `2:3`
C. `3:4`
D. `1:4`

Answer

To find the ratio of the speeds of the truck and the bus, we will follow these steps:

### Step 1: Calculate the speed of the truck
The truck covers a distance of 550 meters in one minute. To find the speed in meters per minute, we can directly use the given distance:
- Speed of the truck = 550 meters/minute

### Step 2: Convert the bus's distance and time into compatible units
The bus covers a distance of 33 kilometers in \( \frac{3}{4} \) hours.
- First, convert kilometers to meters:
- \( 33 \text{ km} = 33 \times 1000 = 33000 \text{ meters} \)
- Next, convert \( \frac{3}{4} \) hours into minutes:
- \( \frac{3}{4} \text{ hours} = \frac{3}{4} \times 60 \text{ minutes} = 45 \text{ minutes} \)

### Step 3: Calculate the speed of the bus
Now we can calculate the speed of the bus using the formula:
- Speed = Distance / Time
- Speed of the bus = \( \frac{33000 \text{ meters}}{45 \text{ minutes}} \)

Calculating this gives:
- Speed of the bus = \( \frac{33000}{45} = 733.33 \text{ meters/minute} \)

### Step 4: Find the ratio of the speeds
Now that we have both speeds:
- Speed of the truck = 550 meters/minute
- Speed of the bus = 733.33 meters/minute

To find the ratio of their speeds:
- Ratio of speed of truck to speed of bus = \( \frac{550}{733.33} \)

To simplify this ratio, we can multiply both the numerator and the denominator by 3 to eliminate the decimal:
- Ratio = \( \frac{550 \times 3}{733.33 \times 3} = \frac{1650}{2200} = \frac{3}{4} \)

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

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