Math Problem Statement
Solution
The problem on the page reads:
A robot can sort 12 boxes in twenty seconds. Working at this rate, how many boxes would be sorted in:
- a) one minute
- b) ten minutes
- c) one hour
Solution Process
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Sorting rate per second: Since the robot sorts 12 boxes in 20 seconds, we can find out how many boxes it sorts per second by dividing 12 by 20:
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a) Number of boxes sorted in one minute (60 seconds): Multiply the rate per second by 60 seconds: So, the robot will sort 36 boxes in one minute.
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b) Number of boxes sorted in ten minutes (600 seconds): Multiply the rate per second by 600 seconds: So, the robot will sort 360 boxes in ten minutes.
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c) Number of boxes sorted in one hour (3600 seconds): Multiply the rate per second by 3600 seconds: So, the robot will sort 2160 boxes in one hour.
Let me know if you need any further explanation! Here are 5 additional related questions to extend your understanding:
- How would the number of boxes change if the sorting speed increased to 15 boxes in 20 seconds?
- If the robot worked for half an hour, how many boxes would it sort?
- How long would it take the robot to sort 1000 boxes?
- What is the sorting rate in boxes per minute?
- How many robots would you need to sort 720 boxes in 10 minutes?
Tip:
When solving rate problems, always find the rate per unit of time (e.g., per second or per minute), as it helps in calculating for different time intervals.
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Math Problem Analysis
Mathematical Concepts
Rate Calculation
Proportions
Unit Conversion (Seconds to Minutes/Hours)
Formulas
Rate per second = Total boxes / Time in seconds
Total boxes = Rate per second * Total time
Theorems
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Suitable Grade Level
Grades 6-8
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