Car M Started driving east from a point p at 8 am.car N started driving from east at point P from 11 am. Theratio of the speeds of m:n is 4 and 5 find geir meeting time

Let's denote the speed of car M as \( 4v \) and the speed of car N as \( 5v \). Car M starts at 8 AM, and car N starts at 11 AM. We need to determine the time at which they meet.

First, we calculate the head start that car M has before car N starts driving. Since car M starts at 8 AM and car N starts at 11 AM, car M has a 3-hour head start. During these 3 hours, car M covers a distance of:
\[ \text{Distance covered by M in 3 hours} = 4v \times 3 = 12v \]

Let \( t \) be the time in hours after 11 AM when cars M and N meet. During this time \( t \), the distance covered by car M is:
\[ \text{Distance covered by M in } t \text{ hours} = 4v \times t \]

The distance covered by car N in the same time \( t \) is:
\[ \text{Distance covered by N in } t \text{ hours} = 5v \times t \]

Since car N starts later and catches up to car M, the total distance covered by car N (including the initial head start of car M) equals the distance covered by car M:
\[ 12v + 4v \times t = 5v \times t \]

Simplifying the equation:
\[ 12v + 4vt = 5vt \]
\[ 12v = 5vt - 4vt \]
\[ 12v = vt \]

Solving for \( t \):
\[ t = \frac{12v}{v} \]
\[ t = 12 \]

Thus, car N will catch up to car M 12 hours after 11 AM, which is 11 PM on the same day.

So, car M and car N will meet at 11 PM.

Would you like more details or have any questions? Here are some related problems:

1. If car M and car N continued driving after meeting, how far would each car have traveled by midnight?
2. How long would it take car N to catch up to car M if car M’s speed was 6v instead?
3. If car N started at 10 AM instead of 11 AM, at what time would they meet?
4. What would be the new meeting time if car M and car N had equal speeds of 4v?
5. If car M had a head start of 4 hours, what would be the new meeting time?
6. How far apart would car M and car N be at 1 PM if car N started at 11 AM as before?
7. What would be the meeting time if car N’s speed was reduced to 3v?
8. If both cars started at 8 AM, how long would it take for car N to overtake car M?

**Tip:** To solve relative motion problems, consider the initial head start and relative speeds of the objects involved. This helps set up the necessary equations to find the meeting time or distance.

Learn how to calculate the meeting time of two cars, M and N, starting at different times and speeds with a 4:5 ratio. This problem involves relative motion and the calculation of distances traveled by each car before meeting. Suitable for advanced high school students.

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