A man left town am at 10:00 AM and traveled by car to town N at an average speed of 72 km/h. He spent 2hours for a meeting and returned through town M by bu...

Answer Details

Let's start by using the formula:

Distance = Speed x Time

For the first part of the journey, the man traveled from town A to town N by car at an average speed of 72 km/h. Let's assume the distance between town A and town N is "d".

Distance from A to N = Speed x Time

d = 72 x t1 (where t1 is the time taken to travel from A to N)

For the second part of the journey, the man traveled from town N to town M by bus at an average speed of 40 km/h. Let's assume the distance between town N and town M is "x".

Distance from N to M = Speed x Time

x = 40 x t2 (where t2 is the time taken to travel from N to M)

We are also given that the distance covered by the bus was 2 km longer than that of the car:

x = d + 2

We know that the total time taken for the entire journey was 3 hours and 55 minutes, which is equivalent to 235 minutes.

Total time taken = t1 + 2 + t2

235 = t1 + 2 + t2

We can now use the equations we have derived to solve for the distance between town M and town N:

d = 72 x t1

x = 40 x t2

x = d + 2

235 = t1 + 2 + t2

We can substitute the third equation into the second equation:

40 x t2 = 72 x t1 + 2

We can then substitute the first equation into the third equation:

40 x t2 = d + 2

We can then substitute the first equation into the second equation:

40 x t2 = 72 x t1 + 2 = d + 2

We can now substitute these equations into the fourth equation:

235 = t1 + 2 + t2

235 = (d + 2)/40 + 2 + d/72

Simplifying this equation, we get:

235 = (9d + 578)/360

Solving for "d", we get:

d = 510

Therefore, the distance between town M and town N is 510 km.