TIME, WORK AND DISTANCE
(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.
(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.
(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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