A car travels 80 km. in 2hours and a a train travels 180 km, in 3 hours. The ratio of the speed of the car to that of the train is

Options

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

Answer

To solve the problem of finding the ratio of the speed of the car to that of the train, we can follow these steps:

### Step 1: Calculate the speed of the car
The formula for speed is given by:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]
For the car:
- Distance = 80 km
- Time = 2 hours

Using the formula:
\[ \text{Speed of the car} = \frac{80 \text{ km}}{2 \text{ hours}} = 40 \text{ km/h} \]

### Step 2: Calculate the speed of the train
Using the same formula for the train:
- Distance = 180 km
- Time = 3 hours

Using the formula:
\[ \text{Speed of the train} = \frac{180 \text{ km}}{3 \text{ hours}} = 60 \text{ km/h} \]

### Step 3: Find the ratio of the speed of the car to the speed of the train
Now we have:
- Speed of the car = 40 km/h
- Speed of the train = 60 km/h

The ratio of the speed of the car to the speed of the train is:
\[ \text{Ratio} = \frac{\text{Speed of the car}}{\text{Speed of the train}} = \frac{40 \text{ km/h}}{60 \text{ km/h}} \]

### Step 4: Simplify the ratio
To simplify the ratio:
\[ \frac{40}{60} = \frac{2}{3} \]

Thus, the ratio of the speed of the car to that of the train is:
\[ \text{Ratio} = 2 : 3 \]

### Final Answer:
The ratio of the speed of the car to that of the train is \(2 : 3\).

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