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 \( t \) for the number of minutes spent running, and solve your inequality for \( t \). In

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 \( 18 + 13.25t \), while for Routine #2, it is simply \( 15.5t \). We want to find out when Routine #1 burns more calories than Routine #2, leading us to the inequality: \[ 18 + 13.25t > 15.5t \] Solving this gives: \[ 18 > 15.5t - 13.25t \] \[ 18 > 2.25t \] \[ t < \frac{18}{2.25} \] \[ t < 8 \] 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!