If a computer printer is capable of printing 4900 monthly credit card bills per hour, while...
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If a computer printer is capable of printing 4900 monthly credit card bills per hour, while a newer model is capable of printing at a rate of 6600 bills per hour, approximately how much longer will the older model take than the new model to print 10,000 bills?
Show answer & explanation
The older model takes 10,000 ÷ 4900 ≈ 2.041 hours ≈ 122.45 minutes to print 10,000 bills. The newer model takes 10,000 ÷ 6600 ≈ 1.515 hours ≈ 90.91 minutes. The difference is approximately 122.45 − 90.91 ≈ 31.54 minutes, which rounds to 31 minutes. However, reviewing the calculation more carefully with rounding: older model ≈ 122.4 min, newer model ≈ 90.9 min, difference ≈ 31.5 min. The closest option is A (81 mins) if interpreted as the absolute time difference under a different calculation method, but the most accurate answer should be approximately 31 mins.
Step-by-step Derivation:
Step 1: Calculate time for older model to print 10,000 bills.
Time = 10,000 bills ÷ 4,900 bills/hour = 2.0408 hours
Convert to minutes: 2.0408 × 60 = 122.45 minutes
Step 2: Calculate time for newer model to print 10,000 bills.
Time = 10,000 bills ÷ 6,600 bills/hour = 1.5152 hours
Convert to minutes: 1.5152 × 60 = 90.91 minutes
Step 3: Find the difference.
Difference = 122.45 − 90.91 = 31.54 minutes ≈ 31 minutes
Note: The provided option set includes E (31 mins) which is the mathematically correct answer. If limited to options A–D only, none precisely match. Option A (81 mins) does not align with this calculation. Please verify the original problem source, as the correct answer should be approximately 31 minutes.