Time and Distance:
Speed = Distance / Time
Average = Total distance travelled/ total time taken
If two bodies are moving in the same direction , then their relative velocity or the speed by which they will overtake one another is equal to the difference of their speeds u- v kmph. If they are travelling in opposite directions then their relative velocity is u + v kmph.
Problems based on trains:
i) When the train, crosses telephone post or a tree, the train will move a distance equal to the length of the train. Therefore, the time taken by a train to cross a tree = length of the train/ Speed of the train
ii) When a train crosses the bridge or a platform the train will have to travel a distance equal to the sum of the lengths of the bridge and train , thus, time taken by train to cross a platform = length of the train + length of the platform / Speed of the train
iii) If two trains a and B are running in the same direction , then the relative speed of the faster train A with respect to the slower train B is the difference between the speeds of the faster train A and the slower train B.
Then the time in which the trains will cross each other is the time taken by the faster train A covering a distance equal to the sum of the lengths of the trains with respect to the relative speed.
Thus, the time taken by the slower train to catch the faster train =
Distance covered in extra time / Difference in Speeds
Time taken to cross each other =
Sum of the lengths of both the trains/ Difference of their speeds
iv) If two trains are running in opposite directions , then the relative speed of the faster train A with respect to the slower train B is the sum of the speeds. They will cross each other at a time equivalent to the time taken in travelling a distance equal to the sum of the lengths of the trains with respect to the relative speed
The time taken to touch each other = Difference in lengths/ Sum of speeds
Time taken to cross each other = sum of lengths/ sum of speeds
v) When a train crosses a man who is walking, two situations arise:
I : when they are moving in the same direction, then the relative speed of the train with respect to the man = Speed of Train - Speed of Man
II: when they are moving in the opposite directions:
Speed of Train + Speed of Man
Rowing Upstream and Downstream:
If a man rows a boat at A kmph in still water and B kmph be the velocity of the current , then the man will row his boat with velocity (a + b) kmph and (a-b) kmph downstream and upstream respectively
Speed of the boat in Downstream direction:
= speed of the boat in still water + speed of the stream.
Speed of the boat in Upstream direction:
= speed of the boat in still water - speed of the stream
Speed of the stream = speed of boat downstream – speed of boat in upstream / 2
Speed of boat in still water = speed of boat downstream + speed of boat in upstream / 2
Monday, April 23, 2007
Time & Work
Time and work:
i) If A completes a work in X days , B in Y days and C in Z days, then
A and B will complete the work in = XY/ X+Y days
A, B and C will complete the work in= XYZ/ XY+YZ+ZX days
ii) If A+B complete the work in X days, B+C in Y days and A+C in Z days then,
A,B,C will complete the work in = 2xyz/ xy+yz+zx days.
A will complete the work in = 2xyz/xy+yz-zx days
iii) A takes N times to complete B and C’s work.
Then A will complete the work in = (n+1) * time taken by A,B and C to complete the work
iv) A’s work/ B’s work = B’s time/ A’s time
v) If A completes a work in X days , B in Y days and C in Z days , then
A and B start a work together , but A leaves the work N days after , then the work will be completed in = (x+n)y/x+y days
If A, B and C start a work together but A leaves the work after N days, then the work will be completed in: = (x+n)yz/xy+yz+zx
If A,B and C start a work together but A stops working N days before the completion of work and B leaves M days before , then the work will be completed by C in = xyz/xy+yz+zx [1+ n/x + m/y]
vi) A completes a work in X days , B in Y days and C in Z days. If all of three start work together but,
A leaves the work after N days then, it would be completed in = yz/y+z [ 1- n/x) days
A leaves the work after N days, B leaves the work in M days , then, it would be completed in:
Z [ 1- n/x – m/x ] days
i) If A completes a work in X days , B in Y days and C in Z days, then
A and B will complete the work in = XY/ X+Y days
A, B and C will complete the work in= XYZ/ XY+YZ+ZX days
ii) If A+B complete the work in X days, B+C in Y days and A+C in Z days then,
A,B,C will complete the work in = 2xyz/ xy+yz+zx days.
A will complete the work in = 2xyz/xy+yz-zx days
iii) A takes N times to complete B and C’s work.
Then A will complete the work in = (n+1) * time taken by A,B and C to complete the work
iv) A’s work/ B’s work = B’s time/ A’s time
v) If A completes a work in X days , B in Y days and C in Z days , then
A and B start a work together , but A leaves the work N days after , then the work will be completed in = (x+n)y/x+y days
If A, B and C start a work together but A leaves the work after N days, then the work will be completed in: = (x+n)yz/xy+yz+zx
If A,B and C start a work together but A stops working N days before the completion of work and B leaves M days before , then the work will be completed by C in = xyz/xy+yz+zx [1+ n/x + m/y]
vi) A completes a work in X days , B in Y days and C in Z days. If all of three start work together but,
A leaves the work after N days then, it would be completed in = yz/y+z [ 1- n/x) days
A leaves the work after N days, B leaves the work in M days , then, it would be completed in:
Z [ 1- n/x – m/x ] days
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