. Abhay and Gourav start moving towards each other, from A to B and B to A respectively, which are 100 km apart. Abhay starts 6 hours after Gourav starts, Abhay meets Gourav 7 hours after Abhay starts. If the speed of Abhay is at least 2 km/h faster than the speed of Gourav, which of the following statement is true?

a. The minimum possible speed of Abhay is 4.3 km/h

b. The maximum possible speed of Abhay is 6.3 km/h

c. The minimum possible speed of Abhay is 6.3 km/h

d. The maximum possible speed of Abhay is 4.3 km/h

Let's denote the speed of Gourav as \( v_G \) km/h and the speed of Abhay as \( v_A \) km/h. 

The key details are:
1. The distance between A and B is 100 km.
2. Abhay starts 6 hours after Gourav.
3. They meet 7 hours after Abhay starts.
4. Abhay's speed is at least 2 km/h faster than Gourav's speed.

### Step 1: Calculate the time taken by Gourav to meet Abhay
Since Abhay meets Gourav 7 hours after he starts, the total time Gourav has been traveling when they meet is:
\[ 7 + 6 = 13 \text{ hours} \]

### Step 2: Express the distances traveled by both
- Distance traveled by Gourav:
\[ \text{Distance by Gourav} = v_G \times 13 \text{ km} \]

- Distance traveled by Abhay:
\[ \text{Distance by Abhay} = v_A \times 7 \text{ km} \]

### Step 3: Use the fact that the sum of these distances equals 100 km
\[ v_G \times 13 + v_A \times 7 = 100 \]

### Step 4: Express \( v_A \) in terms of \( v_G \)
Given that \( v_A \geq v_G + 2 \), we substitute \( v_A = v_G + 2 \) into the equation:
\[ 13v_G + 7(v_G + 2) = 100 \]
Expanding this gives:
\[ 13v_G + 7v_G + 14 = 100 \]
\[ 20v_G = 86 \]
\[ v_G = 4.3 \text{ km/h} \]

Thus, the minimum speed of Gourav is 4.3 km/h, and the minimum speed of Abhay, since \( v_A = v_G + 2 \), is:
\[ v_A = 4.3 + 2 = 6.3 \text{ km/h} \]

### Conclusion
The correct statement is:

**c. The minimum possible speed of Abhay is 6.3 km/h**

Would you like more details or have any questions?

Here are 5 related questions:
1. What would the situation look like if Abhay started earlier than Gourav?
2. How would the scenario change if the distance between A and B was different?
3. How can we calculate the exact time they would meet if their speeds were equal?
4. What would be the impact if one of them took a break during the journey?
5. How would the solution change if their speeds were variable instead of constant?

**Tip:** When working with relative speeds and meeting points, it's helpful to express one variable in terms of another to simplify the equations.

Abhay and Gourav start moving towards each other, from A to B and B to A respectively, which are 100 km apart. Abhay starts 6 hours after Gourav starts, Abhay meets Gourav 7 hours after Abhay starts. If the speed of Abhay is at least 2 km/h faster than the speed of Gourav, which of the following statement is true? a. The minimum possible speed of Abhay is 4.3 km/h b. The maximum possible speed of Abhay is 6.3 km/h c. The minimum possible speed of Abhay is 6.3 km/h d. The maximum possible speed of Abhay is 4.3 km/h

This problem involves calculating the minimum possible speed of Abhay as he meets Gourav on a 100 km journey. The problem explores algebraic concepts, relative speed, and linear equations, making it ideal for students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation