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?
Use for the number of minutes spent running, and solve your inequality for .
In

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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?
Use

for the number of minutes spent running, and solve your inequality for

.
In

UpStudy AI · Accepted Answer

To determine for what amounts of time $$ t $$ spent running Routine #1 burns more calories than Routine #2, let's set up and solve the appropriate inequality. ### Step 1: Define the Calorie Burn for Each Routine 1. **Routine #1:** - **Walking:** Burns a fixed 18 calories. - **Running:** Burns 13.25 calories per minute. Total calories burned in Routine #1: $$ \text{Calories}_{\text{Routine 1}} = 18 + 13.25t $$ 2. **Routine #2:** - **Running Only:** Burns 15.5 calories per minute. Total calories burned in Routine #2: $$ \text{Calories}_{\text{Routine 2}} = 15.5t $$ ### Step 2: Set Up the Inequality We want Routine #1 to burn **more** calories than Routine #2: $$ 18 + 13.25t > 15.5t $$ ### Step 3: Solve the Inequality for $$ t $$ 1. **Subtract** $$ 13.25t $$ from both sides to isolate the terms involving $$ t $$: $$ 18 > 15.5t - 13.25t $$ $$ 18 > 2.25t $$ 2. **Divide** both sides by 2.25 to solve for $$ t $$: $$ \frac{18}{2.25} > t $$ $$ 8 > t $$ This can also be written as: $$ t < 8 $$ ### Step 4: Interpret the Solution The inequality $$ t < 8 $$ means that **if Reuben spends less than 8 minutes running**, Routine #1 will burn more calories than Routine #2. ### Conclusion $$ t < 8 \text{ minutes} $$ **Therefore, Routine #1 burns more calories than Routine #2 when Reuben runs for less than 8 minutes.** Reuben should run for less than 8 minutes for Routine #1 to burn more calories than Routine #2.

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