Solve the Problem by Writing and Solving a Suitable System $\mathrm{C}$

Solve the problem by writing and solving a suitable system of equations.
-Jane wants to buy a photocopier. The salesperson has the following information on 3 models. If all 3 are used, a specific job can be done in 50 minutes. If copier A operates for 20 minutes and copier B for 50 minutes, one-half the job is finished. If copier B operates for 30 minutes and copier $\mathrm{C}$ for 80 minutes, three-fifths of the job is done. Which is the fastest copier, and how long does it take for this copier to finish the whole job?

A) $C$ is fastest; 120 minutes
B) C is fastest; 100 minutes
C) B is fastest; 100 minutes
D) A is fastest; 120 minutes