TIME, WORK AND DISTANCE
Important results
(i) Speed = distance/Time
(ii) Time = Distance /Speed
(iii) Distance = Speed x Time
1 km/hr = 5/18 m/s
1 m/s = 18/5 km/hr.
IMPORTANT POINTS
(1) If A can finish a piece of work in n days, the work done by A in 1 day = 1/n
(2) If A's 1 day's work =1/n , then the time taken by A to finish the work = n days.
(3) In a storage tank, the pipe which fills it is called an inlet pipe while the pipe that empties it is called as an outlet pipe.
(4) If an inlet pipe fills a tank in x hours, then the work done by it in 1 hour = -1/y
(5) If an outlet pipe empties a full tank in y hours, then the work done by it in 1 hour = -1/y
TIME AND DISTANCE
Uniform speed: If equal distances are covered in equal intervals of time, then speed is said to be uniform or constant.
Relative speeds:
(1) If two bodies are moving in opposite direction towards each other with speed x km/hr and Y km/hr respectively then (x + y) km/hr is called their relative speed.
(2) If two bodies are moving in same direction with speed x km/hr and y km/hr respectively then (x - y) km/hr is called their relative speed.
Note: For Boat or Rivers:
(3) Relative speed in same direction is (x + y) km/hr.
(4) Relative speed in opposite direction is (x - y) km/hr.
IMPORTANT POINTS HELP TO SOLVE THE PROBLEMS
(A) If a train of length l metres is moving at x km/hr then
(i) the time taken to cover a stationary object is the time taken l by the train to cover l metres at x km/hr.
(ii) the time taken to cover a stationary object (of length b) is the time taken by the train to cover (l + b) metres at x km/hr.
(iii) When two trains of length l metres and b metres are moving in opposite direction with a speed of x km/hr and y km/hr respectively, then the time taken by them to cross each other is the time taken to cover (l + b) metres with the relative speed (x + y) km/hr.
(iv) When two trains of length l metres and b metres are moving in the same direction with a speed of x km/hr and y km/hr respectively when x > y, then, the time taken by faster train to cross the slower train is the time taken to cover (l + b) metres at a relative speed of (x - y) km/hr.
(B) The time taken by a train of length l metres moving at x km/hr to cross a man running at y km/hr.
(i) in the same direction, is the time taken to cover l metres with a speed of (x - y) km/hr.
(ii) in the opposite direction, is the l time taken to cover l metres with a speed of (x + y) km/hr.
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