Problem: A train travelling at 60kmph crosses cyclist who is cycling at 12 kmph in opposite direction in 20sec find time taken by train to cross another cyclist travelling at 20 kmph in same direction?

Solution:

Understanding the problem:
We are given the following information:
- Speed of train = 60 kmph
- Speed of cyclist in opposite direction = 12 kmph
- Time taken to cross the cyclist in opposite direction = 20 sec
We need to find the time taken by the train to cross another cyclist travelling at 20 kmph in the same direction.

Approach:
We can use the concept of relative speed to solve this problem. When two objects are moving in the same direction, their relative speed is the difference between their speeds. When they are moving in opposite directions, their relative speed is the sum of their speeds.

Calculations:
Let us assume the length of the train to be L meters and the time taken to cross the cyclist in the same direction to be t seconds.
Relative speed of train and cyclist = (60 + 20) kmph = 80 kmph = (80 * 5) / 18 m/s = 200 / 9 m/s
Distance covered by the train in crossing the cyclist in the opposite direction = L + length of the cyclist
Distance = speed * time
(L + length of the cyclist) = (60 + 12) * (20 / 3600)
L + length of cyclist = 1 km
L = (1 - length of cyclist) = (1000 - 12) = 988 meters
Relative speed of train and cyclist in the same direction = (60 - 20) kmph = 40 kmph = (40 * 5) / 18 m/s = 100 / 9 m/s
Distance covered by the train in crossing the cyclist in the same direction = L + length of the cyclist
Distance = speed * time
L + length of cyclist = (60 - 20) * (t / 3600)
L + length of cyclist = (4 / 9) * t
Substitute the value of L from the previous calculation
988 + 12 = (4 / 9) * t
t = (1000 / 3) seconds

Answer:
The time taken by the train to cross another cyclist travelling at 20 kmph in the same direction is (1000 / 3) seconds or approximately 333.33 seconds.