Time work and Distance, Mathematics Assignment Help

mathematics - Time work and Distance, Mathematics

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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