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

Time, Speed and Distance

Equation

Important Conversion Factors:

Equation

Average Speed

  • Equation

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

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

Relative Speed

For Trains

  • Equation

For Boats and Streams

  • Equation

  • Equation

Time and Work

  • Equation

Time & Work

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

  • If A’s 1 day’s work Equation 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 Equation Ratio of times taken by Equation to finish a work Equation

Pipes & Cisterns

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