a person can copy the final exam in 28 minutes using a new copy machine. using an old copy machine, it takes 70 minutes. if both machines are used, how long will it take to complete the job
1/b = 1/28 + 1/70
b = ?
2.5
To calculate how long it will take to complete the job using both machines, we need to determine their combined efficiency.
Let's denote the efficiency of the new copy machine as "x" (amount of work it can complete in 1 minute), and the efficiency of the old copy machine as "y" (amount of work it can complete in 1 minute).
From the given information, we know that:
- The new copy machine can copy the final exam in 28 minutes, so its efficiency is 1/28 (1 exam per 28 minutes).
- The old copy machine can copy the final exam in 70 minutes, so its efficiency is 1/70 (1 exam per 70 minutes).
To find their combined efficiency, we can add their individual efficiencies:
x + y = 1/28 + 1/70
To add these two fractions, we need to find a common denominator:
x + y = (70 + 28) / (70 * 28)
x + y = 98 / 1960
x + y = 1/20
Therefore, the combined efficiency of both machines is 1/20 (1 exam per 20 minutes).
Now, to find the time it will take to complete the job, we can use the formula:
Time = Total Work / Combined Efficiency
Since the job is to copy 1 final exam, the Total Work is 1.
Time = 1 / (1/20)
Time = 20 minutes
Therefore, it will take 20 minutes to complete the job using both machines.
To find out how long it will take to complete the job using both machines, we need to calculate the time it would take for each machine individually and then add those times together.
Let's assume that if the new copy machine takes 28 minutes to copy the final exam, it can make 1/28th of the copies per minute. Similarly, if the old copy machine takes 70 minutes to copy the final exam, it can make 1/70th of the copies per minute.
To find out how many copies both machines can make per minute, we can add up the rates at which each machine makes copies:
1/28 + 1/70
To add these fractions, we need to find a common denominator, which in this case is 140:
(1/28) + (1/70) = (5/140) + (2/140) = 7/140
So, both machines can make 7/140th of the final exam copies per minute.
To find out how long it will take to complete the job, we need to find the reciprocal of the fraction 7/140, which represents the number of minutes required to complete one copy of the exam:
140/7 = 20
Therefore, it would take both machines 20 minutes to complete the job if used together.