Certainly! Below is a step-by-step solution for the problem, along with the corresponding LaTeX code.
### Steps to the Solution
1. **Define Variables**:
Let \( a \) be the time taken by the first pipe to fill the cistern, \( a \) also be the time taken by the second pipe to fill the cistern (since they have equal volume), and let \( b \) be the time taken by the third pipe to fill the cistern.
2. **Rate of Work**:
The rate of work for