Bill needs to make a large number of photocopies. Copier 1 alone can make the copies in 4 hours while copier 2 alone can complete the job in 3 hours. If Bill runs the two photocopiers at once, how long will it take to complete the photocopying job?
Question
Bill needs to make a large number of photocopies. Copier 1 alone can make the copies in 4 hours while copier 2 alone can complete the job in 3 hours. If Bill runs the two photocopiers at once, how long will it take to complete the photocopying job?
Solution
To solve this problem, we need to find the combined rate of the two copiers.
Step 1: Find the rate of each copier. The rate of copier 1 is 1 job per 4 hours, or 1/4 of the job per hour. The rate of copier 2 is 1 job per 3 hours, or 1/3 of the job per hour.
Step 2: Add the rates together to find the combined rate. The combined rate of the two copiers is 1/4 + 1/3 = 3/12 + 4/12 = 7/12 of the job per hour.
Step 3: Find the time it takes for the two copiers to complete the job together. To find the time, divide the total job (1 job) by the combined rate (7/12 of the job per hour). So, the time it takes for the two copiers to complete the job together is 1 / (7/12) = 12/7 hours, which is approximately 1.71 hours.
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