Question
Solving a decimal word problem using a linear Inequallty with the variabl…
Reuben is choosing between two exercise routines.
In Routine #1, he burns 18 calories walking. He then runs at a rate that burns 13.25 calories per minute.
In Routine #2, he does only running, burning 15.5 calories per minute.
For what amounts of time spent running will Routine #1 burn more calories than Routine #2?
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Reuben is choosing between two exercise routines.
In Routine #1, he burns 18 calories walking. He then runs at a rate that burns 13.25 calories per minute.
In Routine #2, he does only running, burning 15.5 calories per minute.
For what amounts of time spent running will Routine #1 burn more calories than Routine #2?
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Ask by Estrada Mullins. in the United States
Jan 23,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
Reuben should run for less than 8 minutes for Routine #1 to burn more calories than Routine #2.
Solution
To determine for what amounts of time
Step 1: Define the Calorie Burn for Each Routine
-
Routine #1:
- Walking: Burns a fixed 18 calories.
- Running: Burns 13.25 calories per minute.
Total calories burned in Routine #1: -
Routine #2:
- Running Only: Burns 15.5 calories per minute.
Total calories burned in Routine #2:
Step 2: Set Up the Inequality
We want Routine #1 to burn more calories than Routine #2:
Step 3: Solve the Inequality for
-
Subtract
from both sides to isolate the terms involving : -
Divide both sides by 2.25 to solve for
: This can also be written as:
Step 4: Interpret the Solution
The inequality
Conclusion
Therefore, Routine #1 burns more calories than Routine #2 when Reuben runs for less than 8 minutes.
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution Extra Insights
To analyze the calorie burn for Reuben’s routines, we can set up the following inequality for Routine #1 and Routine #2. In Routine #1, the total calories burned can be expressed as
Solving this gives:
So, Reuben can run for up to 8 minutes before Routine #1 isn’t burning more calories than Routine #2!
When thinking about calories burned during exercise, it’s fascinating to consider how different activities have varying calorie burn rates. For example, running tends to burn more calories than walking due to the increased intensity and muscle engagement. This is why many fitness enthusiasts prefer running for weight loss or improved cardiovascular health.
Many people unknowingly make the mistake of underestimating the time spent exercising when comparing different routines. To avoid this, it’s crucial to clearly define how long you’ll be engaging in each part of your workout. Calculating total calorie burn requires careful attention to both activity duration and intensity!
