13. Pipes and Cistern problems
13. Pipes and Cistern problems Home page of Arithmetic Problems Below are 10 pipes and cisterns problems, each with a step-by-step solution procedure and detailed explanation. Pipes and cisterns problems are a subset of work rate problems, focusing on the rate at which pipes fill or empty tanks (cisterns). The key concept is work rate , where the rate is the fraction of the tank filled or emptied per unit of time (e.g., tanks per hour). The standard formulas are: Work (tank fraction) = Rate × Time Rate = Work / Time Time = Work / Rate Filling pipe rate : Positive (e.g., 1/10 tank/hour if it fills in 10 hours) Emptying pipe/leak rate : Negative (e.g., -1/15 tank/hour if it empties in 15 hours) Combined rate : Sum of individual rates (positive for filling, negative for emptying) Work is typically normalized to 1 tank (full tank = 1). Problems may involve multiple filling pipes, emptying pipes, leaks, staggered starts, or partial filling. Units are usually hours or minutes for ...
