A tractor is moving with a speed of 20 km/hour , x km ahead of a truch moving with a speed of 35 km/hour . If it takes 20 minutes for a truck to overtake the tractor , then what is x equal to?

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Understand the problem
We have a tractor moving at a speed of 20 km/h and a truck moving at a speed of 35 km/h. The truck is trying to overtake the tractor, and we need to find out how far ahead the tractor is (denoted as x km) when it takes the truck 20 minutes to overtake the tractor.

### Step 2: Convert time from minutes to hours
Since the speeds are given in km/h, we need to convert the time taken from minutes to hours.
- Time taken = 20 minutes = \( \frac{20}{60} \) hours = \( \frac{1}{3} \) hours.

### Step 3: Calculate the distance covered by the truck
Using the formula for distance:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
For the truck:
- Speed of the truck = 35 km/h
- Time = \( \frac{1}{3} \) hours

So, the distance covered by the truck in 20 minutes is:
\[ \text{Distance}_{\text{truck}} = 35 \times \frac{1}{3} = \frac{35}{3} \text{ km} \]

### Step 4: Calculate the distance covered by the tractor
Using the same formula for the tractor:
- Speed of the tractor = 20 km/h
- Time = \( \frac{1}{3} \) hours

So, the distance covered by the tractor in 20 minutes is:
\[ \text{Distance}_{\text{tractor}} = 20 \times \frac{1}{3} = \frac{20}{3} \text{ km} \]

### Step 5: Set up the equation
When the truck overtakes the tractor, the distance covered by the truck is equal to the distance covered by the tractor plus the distance x (the initial distance between them).
\[ \text{Distance}_{\text{truck}} = \text{Distance}_{\text{tractor}} + x \]
Substituting the distances we calculated:
\[ \frac{35}{3} = \frac{20}{3} + x \]

### Step 6: Solve for x
To find x, we can rearrange the equation:
\[ x = \frac{35}{3} - \frac{20}{3} \]
Finding a common denominator (which is already 3):
\[ x = \frac{35 - 20}{3} = \frac{15}{3} = 5 \text{ km} \]

### Final Answer
Thus, the value of x is 5 km.

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