Rate Problems: Speed, Work, Pipes and Cistern Tricks and Formulas

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Time, Speed and Distance

Important Conversion Factors:

Average Speed

  • If the distance is constant, then average speed is given by harmonic mean of two speeds:

  • If the time is constant, then average speed is given by arithmetic mean of two speeds

Relative Speed

For Trains

For Boats and Streams

Time and Work

Time & Work

  • If A can do a piece of work in n days, then A’s 1 day’s work

  • If A’s 1 day’s work then A can finish the work in n days.

  • If A is thrice as good a workman as B, then: Ratio of work done by A and Ratio of times taken by to finish a work

Pipes & Cisterns

If a pipe can fill a tank in ‘x’ hours and another pipe can empty the full tank in ‘y’ hours then on opening both the pipes, the net part of the tank filled in 1 hour is