High speed copier works three times as fast as a regular copier.
When both copiers are used, they can copy a group of documents in 12 minutes.
How long would each copier require to do the copying alone
let T be the time for the reg copier to make one document, and T/3 the time for the HSpeed.
task= rate*time=
group= (group/T + 3group/T)*12
1/12= 4/T
T=48min
T/3=16min
To solve this problem, we can use the concept of work rate.
Let's assume the regular copier's work rate is 1 document per minute. Therefore, the high-speed copier's work rate would be 3 documents per minute since it can copy three times as fast.
Let's say the regular copier takes x minutes to copy the group of documents alone. In that time, it would have completed x documents.
Similarly, the high-speed copier would require x/3 minutes to copy the same group of documents alone, completing (x/3) * 3 = x documents.
When both copiers are used together, they can complete the group of documents in 12 minutes. Therefore, their combined work rate would be (1/x) + (3/(x/3)) = 1/12 documents per minute.
To solve this equation, we can find a common denominator and simplify it:
(x + 9) / x = 1/12
Cross-multiplying:
12(x + 9) = x
Expanding:
12x + 108 = x
Rearranging the equation:
12x - x = -108
Simplifying:
11x = -108
Dividing both sides by 11:
x = -108/11
The regular copier cannot have a negative time, so we can discard this solution. It means that the regular copier cannot complete the task alone.
However, the high-speed copier requires (x/3) = (-108/11)/3 = -36/11 minutes to complete the copying alone.
Since time cannot be negative, we need to discard this solution as well.
Therefore, there is no valid solution in this context.