The distance between two cities P and Q is $900 ext{ km}$. Car A and Car B can cover this distance in $X$ hours and $(X + 4)$ hours respectively. Car B starts from city P at 6:00 am, and Car A starts from the same city at 8:00 am. Both cars meet at 10:30 am. What is the distance between city P and the point where both cars meet?

Question

The distance between two cities P and Q is $900 	ext{ km}$. Car A and Car B can cover this distance in $X$ hours and $(X + 4)$ hours respectively. Car B starts from city P at 6:00 am, and Car A starts from the same city at 8:00 am. Both cars meet at 10:30 am. What is the distance between city P and the point where both cars meet?

Accepted Answer

**Solution:**

1. Let the speed of Car A be $\frac{900}{X} 	ext{ km/h}$ and the speed of Car B be $\frac{900}{X+4} 	ext{ km/h}$.

2. Car B starts at 6:00 am and meets Car A at 10:30 am, so Car B travels for $4.5$ hours.

3. Car A starts at 8:00 am and meets Car B at 10:30 am, so Car A travels for $2.5$ hours.

4. Let the meeting point be at a distance $D$ km from city P.

5. Distance covered by Car B in $4.5$ hours is:
   $$	ext{Distance}_B = \frac{900}{X+4} 	imes 4.5$$

6. Distance covered by Car A in $2.5$ hours is:
   $$	ext{Distance}_A = \frac{900}{X} 	imes 2.5$$

7. Since both meet at the same point,
   $$\frac{900}{X+4} 	imes 4.5 = \frac{900}{X} 	imes 2.5$$

8. Simplify the equation:
   $$\frac{4.5}{X+4} = \frac{2.5}{X}$$

9. Cross-multiplied:
   $$4.5X = 2.5(X + 4)$$

10. Expand and simplify:
    $$4.5X = 2.5X + 10$$
    $$4.5X - 2.5X = 10$$
    $$2X = 10$$
    $$X = 5$$

11. Speed of Car A:
    $$\frac{900}{5} = 180 	ext{ km/h}$$

12. Distance covered by Car A in $2.5$ hours:
    $$180 	imes 2.5 = 450 	ext{ km}$$

13. Therefore, the meeting point is $450 	ext{ km}$ from city P.

**Answer:** $450 	ext{ km}$

Answer

Answer

Answer

Answer