The average speed of a train is `4(1)/(3)` times the average speed of a tractor. The tractor covers 270 km in 15 hours. How much distance will the train cover in 12 hours?

Options

A. 654 km
B. 896 km
C. 564 km
D. 936 km

Answer

To solve the problem step by step, we will first find the average speed of the tractor, then determine the average speed of the train, and finally calculate the distance the train will cover in 12 hours.

### Step 1: Calculate the average speed of the tractor
The average speed of the tractor can be calculated using the formula:

\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]

Given that the tractor covers 270 km in 15 hours:

\[ \text{Speed of tractor} = \frac{270 \text{ km}}{15 \text{ hours}} = 18 \text{ km/h} \]

### Step 2: Determine the average speed of the train
According to the problem, the average speed of the train is \(4 \frac{1}{3}\) times the average speed of the tractor. We first convert \(4 \frac{1}{3}\) into an improper fraction:

\[ 4 \frac{1}{3} = \frac{13}{3} \]

Now, we can find the speed of the train:

\[ \text{Speed of train} = \left(\frac{13}{3}\right) \times \text{Speed of tractor} = \left(\frac{13}{3}\right) \times 18 \text{ km/h} \]

Calculating this gives:

\[ \text{Speed of train} = \frac{13 \times 18}{3} = \frac{234}{3} = 78 \text{ km/h} \]

### Step 3: Calculate the distance covered by the train in 12 hours
Now that we have the speed of the train, we can calculate the distance it covers in 12 hours using the formula:

\[ \text{Distance} = \text{Speed} \times \text{Time} \]

Substituting the values we have:

\[ \text{Distance covered by train} = 78 \text{ km/h} \times 12 \text{ hours} = 936 \text{ km} \]

### Final Answer
The train will cover **936 km** in 12 hours.

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