A car travels 288 km in 4 hours and a train travels 540 km in 6 hours. The ratio of their speeds is

Options

A. 5:4
B. 4:5
C. 5:6
D. 3:5

Answer

To solve the problem of finding the ratio of the speeds of a car and a train, we can follow these steps:

### Step 1: Calculate the speed of the car
The formula for speed is:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]
For the car:
- Distance = 288 km
- Time = 4 hours

Using the formula:
\[ \text{Speed of car} (V_c) = \frac{288 \text{ km}}{4 \text{ hours}} = 72 \text{ km/h} \]

### Step 2: Calculate the speed of the train
Using the same formula for the train:
- Distance = 540 km
- Time = 6 hours

Using the formula:
\[ \text{Speed of train} (V_t) = \frac{540 \text{ km}}{6 \text{ hours}} = 90 \text{ km/h} \]

### Step 3: Find the ratio of the speeds
Now that we have the speeds of both the car and the train, we can find the ratio:
\[ \text{Ratio of speeds} = \frac{V_c}{V_t} = \frac{72 \text{ km/h}}{90 \text{ km/h}} \]

### Step 4: Simplify the ratio
To simplify the ratio:
\[ \frac{72}{90} = \frac{72 \div 18}{90 \div 18} = \frac{4}{5} \]

### Final Answer
The ratio of the speeds of the car to the train is:
\[ \text{Ratio} = 4:5 \]

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