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.