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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:
- 20x + 50y = 1/2
- 50y + 80z = 3/5
- 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.
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