College

Jane wants to buy a photocopier. The salesperson has the following information on 3 models:

1. If all 3 are used, a specific job can be done in 50 minutes.
2. If copier A operates for 20 minutes and copier B for 50 minutes, one-half the job is finished.
3. If copier B operates for 30 minutes and copier 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?

Answer :

Final answer:

Copier A is the fastest, and it takes 20 minutes to finish the whole job.

Explanation:

Let's assign variables to represent the speed of photocopiers.

Let x be the speed of copier A, y be the speed of copier B, and z be the speed of copier C.

From the given information, we can set up a system of equations:

  1. 20x + 50y = 1/2
  2. 50y + 80z = 3/5
  3. 20x + 50y + 80z = 1 (representing the whole job)

Solving this system of equations, we find that x = 1/140, y = 1/70, and z = 3/560.

Since the speed is inversely proportional to the time taken, the copier with the smallest speed is the fastest.

Therefore, copier A is the fastest.

To find the time it takes for copier A to finish the whole job, we substitute the value of x into the third equation:

20(1/140) + 50(1/70) + 80z = 1.

Solving for z, we get z = 1/560.

Therefore, copier A takes 20 minutes to finish the whole job.

Learn more about Photocopiers here:

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