Arun and Barun run with the speeds of 30 m/s and 20 m/s around a circular track of 600 m. They participate in a 3000 m race. What is the distance covered by Arun when he passes Barun for the 5 th time?

Options

A. 2200 m
B. 2250 m
C. 2850 m
D. none of these

Answer

To solve the problem, we need to determine the distance covered by Arun when he passes Barun for the 5th time during their race on a circular track. Here’s the step-by-step solution:

### Step 1: Understand the Speeds and Track Length
Arun runs at a speed of 30 m/s and Barun runs at a speed of 20 m/s. The length of the circular track is 600 m.

**Hint:** Identify the speeds of both runners and the length of the track.

### Step 2: Calculate the Relative Speed
Since both runners are running in the same direction, we need to calculate their relative speed. The relative speed is given by the difference in their speeds:

\[ \text{Relative Speed} = \text{Speed of Arun} - \text{Speed of Barun} = 30 \, \text{m/s} - 20 \, \text{m/s} = 10 \, \text{m/s} \]

**Hint:** When two objects move in the same direction, their relative speed is the difference of their speeds.

### Step 3: Determine the Time to Meet for the First Time
To find out how long it takes for Arun to pass Barun for the first time, we can use the formula:

\[ \text{Time} = \frac{\text{Distance}}{\text{Relative Speed}} = \frac{600 \, \text{m}}{10 \, \text{m/s}} = 60 \, \text{seconds} \]

**Hint:** Use the distance of one complete lap (the track length) to find the time taken to meet for the first time.

### Step 4: Calculate the Time to Meet for the Fifth Time
Since the time taken to meet for each subsequent time remains the same (because they are running at constant speeds), the time taken for Arun to pass Barun for the 5th time is:

\[ \text{Time for 5th meeting} = 5 \times \text{Time for 1st meeting} = 5 \times 60 \, \text{seconds} = 300 \, \text{seconds} \]

**Hint:** Multiply the time taken for the first meeting by the number of times they meet to find the total time for the fifth meeting.

### Step 5: Calculate the Distance Covered by Arun
Now, we can calculate the distance covered by Arun in this time using the formula:

\[ \text{Distance} = \text{Speed} \times \text{Time} = 30 \, \text{m/s} \times 300 \, \text{s} = 9000 \, \text{meters} \]

**Hint:** Use the formula for distance (speed multiplied by time) to find out how far Arun has run.

### Final Answer
The distance covered by Arun when he passes Barun for the 5th time is **9000 meters**.