Chapter 9.1, Problem 64PE

For Exercises 61-64, set up a system of linear equations to represent the scenario. Solve the system by using Gaussian elimination or Gauss-Jordan elimination.

Three pumps ( $A$ , $B$ , and $C$ ) work to drain water from a retention pond. Working together the pumps can pump $1500\text{ gal/hr}$ of water. Pump $C$ works at a rate of $100\text{ gal/hr}$ faster than pump $B$ . In $3\text{ hr}$ , pump $C$ can pump as much water as pumps $A$ and $B$ working together in $2\text{ hr}$ . Find the rate at which each pump works.