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

## 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

## 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