Reported can be printed in 55 minutes by one machine.
A second machine can print the report in 66 minutes.
How long will it take to print the report with both machines operating?
To find out how long it will take to print the report with both machines operating, we need to calculate their combined printing rate.
Let's denote the printing rate of the first machine as R1 (in reports per minute) and the printing rate of the second machine as R2 (in reports per minute).
From the given information, we know that the first machine can print the report in 55 minutes, which means its printing rate is 1/55 reports per minute (R1 = 1/55).
Similarly, the second machine can print the report in 66 minutes, so its printing rate is 1/66 reports per minute (R2 = 1/66).
To calculate the combined printing rate, we add the rates of both machines:
Combined printing rate = R1 + R2
= 1/55 + 1/66 (since the rates are in reports per minute)
To add these fractions, we need to find a common denominator. The least common multiple of 55 and 66 is 330.
= (6/330) + (5/330) (multiplying the fractions by appropriate factors to get the common denominator)
= 11/330
So, the combined printing rate of both machines is 11/330 reports per minute.
To find out how long it will take to print the report with both machines operating, we divide the total number of reports (1) by the combined printing rate:
Time taken = Total number of reports / Combined printing rate
= 1 / (11/330)
= 330/11
= 30
Therefore, it will take 30 minutes to print the report with both machines operating.
To find out how long it will take to print the report with both machines operating, we can use the concept of rates.
Let's say that the first machine can print at a rate of 1 report per 55 minutes, and the second machine can print at a rate of 1 report per 66 minutes.
In one minute, the first machine can complete 1/55th of the report, and the second machine can complete 1/66th of the report.
Now, to find the combined rate of the two machines, we add their individual rates: 1/55 + 1/66.
To simplify this, we can find the least common multiple (LCM) of 55 and 66, which is 330. This means that in 330 minutes, both machines would have completed a whole number of reports.
Now, we can calculate the combined rate of the two machines in terms of reports per minute: (66 + 55) / 330 = 121 / 330.
So, both machines together can complete 121/330th of the report in one minute.
To find out how long it will take to complete the entire report, we can take the reciprocal of the combined rate: 330 / 121.
Therefore, it will take approximately 2.727 hours, or 2 hours and 44 minutes, to print the report with both machines operating.