find the new photocopier alone would take and the old photocopier would take.

Question

a new photocopier works 2 times a fast as an old one. When the machines work together, it can produce all its manuals in 16 hours. Find the time it would take each machines, working alone to complete the job.

Answer 1

Since we don't know the amount of time that each copier can complete the job individually, we can represent the times with the variable t

 

The old photocopier can complete the job in t hours

 

The new photocopier can complete the job in 1/2 t = t/2 hours

 

Together, the two machines can complete the job in 16 hours. That means that the two can complete 1/16 of the job in 1 hour. 

 

Using that logic, the old photocopier can complete 1/t of the job in 1 hour. 

 

The new photocopier can complete 1/(t/2) = 2/t of the job in 1 hour. (twice as fast)

 

We can now set up the following equation:

 

1/t + 2/t = 1/16  (Multiply both sides of the equation by the common denominator 16t)

 

16 + 32 = t

 

48 = t

 

The old photocopier can print all the manuals in 48 hours working alone

 

The new photocopier can print all the manuals in t/2 = 48/2 = 24 hours working alone

 

 

 

 

Answer 2

1. Photocopy rate of the first copier =  X (manuals/hr)
2. Photocopy rate of the second copier = 2X (manuals/hr)
3. If we add X + 2X, we get the total number of manuals produced in an hour.  But this question doesn't tell us how many manuals were produced;  only that it took 16 hours.  So, how many manuals were produced in 16 hours?  Just take the total rate of X+2X, which is the number of manuals per hour produced by both photocopiers, and multiply it by 16 hours.
1. Let M  = total number of manuals produced in 16 hours
2. M= (X+2X)*16
3. M  = 3X*16
4. M  = 48X
4. Now to find how long it would take each copier to produce 48X worth of manuals, simply divide it by the rate:
1. For the first copier :  T1 = M/X where T1 is the time required by the first copier to produce M number of manuals
2. T1 = 48X/ X = 48 hours  
3. Similarly, for the second copier:  T2 = M/2X =  48X/2X = 24 hours