A manuscript needs to be printed. One printer can do the job in 60 minutes and the other can do it in 40 minutes. How long would it take if both printers were used?
they each do a fraction of the job
(t / 40) + (t / 60) = 1
To determine the time it would take if both printers were used, we need to calculate the "combined rate" at which they can complete the job. The combined rate of two machines working together can be calculated using the formula:
1 / combined rate = 1 / time required for the first machine + 1 / time required for the second machine
Let's plug in the values:
1 / combined rate = 1 / 60 + 1 / 40
To simplify the equation, let's find a common denominator of 120:
1 / combined rate = 2 / 120 + 3 / 120
Combining the fractions:
1 / combined rate = 5 / 120
Now, let's invert both sides of the equation:
combined rate = 120 / 5
Simplifying further:
combined rate = 24
Therefore, the combined rate of both printers is 24 manuscript per minute.
To find the time it would take to finish the job, we can divide the total manuscript count by the combined rate:
time taken = manuscript count / combined rate
Since we were not given the manuscript count in the question, we cannot calculate an exact time. However, if we are given the manuscript count, we can easily calculate the time taken.