How many times the two cars meet each other?

Question

A and B are two towns 100 km apart. M starts from A and travel towards B and N starts from B and travel towards A respectively at 20 and 25 km/hr respectively. Upon reaching their destinations, they turn back and continue to repeat the journey. How many times do they meet in 24 hours if they start at the same time?

As the car N will travel 600 KM i.e. 6 journeys (3 rounds) in 24 Hours, the answer 6 times feels logical as it will definitely cross the other car M at every journey.

Am i correct, or i am missing something.

Answer 1

Some problems lend themselves to graphical analysis.

In the graph, the X axis is time in hours. The Y axis is the distance from $A$ in kilometers. The line starting at $(0,0)$ traces $M$'s path. The line starting at $(0,100)$ traces $N$'s path. Where the lines cross, the travelers meet.

Answer 2

The first time those two cars met they had traveled a combined 100 kms. From here on they met every 200 combined kms traveled (why?). After 24 hours they had traveled a combine of $1080=100+200\times 4+180$ kms i.e. they have met 5 times.