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

Time, Speed and Distance


Important Conversion Factors:


Average Speed

  • AverageSpeed=TotaldistancetravelledTotaltimetaken=d1+d2+d3+t1+t2+t3+

  • If the distance is constant, then average speed is given by harmonic mean of two speeds: Savg=2s1s2s1+s2

  • If the time is constant, then average speed is given by arithmetic mean of two speeds Savg=s1+s22

Relative Speed

For Trains

  • Time=sumofthelengthsRelativespeed=L1+L2s1±s2

For Boats and Streams

  • sdownstream=Sboat+Sstream

  • supstream=SboatSstream

Time and Work

  • Numberofdaystocompletethework=1workdoneinoneday

Time & Work

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

  • If A’s 1 day’s work =1/n, 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 B=3:1, Ratio of times taken by A&B to finish a work =1:3

Pipes & Cisterns

  • If a pipe can fill a tank in ‘x’ hours and another pipe can empty the full tank in ‘y’ hours (wherey>x), then on opening both the pipes, the net part of the tank filled in 1 hour is (1x1y)