Math Problem Statement

A cistern can be filled in 20 minutes and 30 minutes by two pipes, A and B, respectively and emptied in 40 minutes by a third pipe, C. How long would it take to fill the cistern when all three pipes are released simultaneously?

Solution

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Math Problem Analysis

Mathematical Concepts

Rate of Work
Algebra
Fractions

Formulas

Net rate = Rate of filling - Rate of emptying
Rate of filling (Pipe A) = 1/20 units per minute
Rate of filling (Pipe B) = 1/30 units per minute
Rate of emptying (Pipe C) = 1/40 units per minute
Time = 1 / Net rate

Theorems

Work-Rate Problems

Suitable Grade Level

Grades 8-10