Question

Mary Gordon is training for a triathlon. Like most triathletes she regularly trains in two of the three events every day. On Saturdays she expects to burn about 800 calories during her workout by running and swimming. Running: 7.1 calories per minute Swimming: 10.1 calories per minute Bicycling: \(\quad 6.2\) calories per minute Copy and complete the model below. Let \(x\) represent the number of minutes she spends running, and let \(y\) represent the number of minutes she spends swimming.

Short answer

The equation representing this situation is \(7.1x + 10.1y = 800\), where \(x\) is the total time Mary spends running and \(y\) is the total time she spends swimming.

Step-by-step solution

Understanding the problem

Mary Gordon wants to burn exactly 800 calories on Saturdays by performing two activities: running and swimming. For running, she burns 7.1 calories per minute and for swimming, she burns 10.1 calories per minute. We must determine the equation that represents this situation.

Formulate the equation

Let \(x\) represent the total time (in minutes) that Mary spends running, and \(y\) represent the total time she spends swimming. Since calories burned is the product of the rate of burning (calories minute) and time, we can express the situation as the equation: 7.1x + 10.1y = 800.

Simplify the equation

The given equation is already in its simplest form. This equation represents the relationship between the time spent on running and swimming (in minutes) needed for Mary to burn 800 calories.