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 bus at an average speed of 40KM/H.
If the distance covered by the bus was 2km longer than that of the car and he arrived at town M at 1 :55PM.
calculate distance from M to N.
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.