Chapter 5.1, Problem 27E

To determine

To find: the time spent on each machine

Answer to Problem 27E

Thus, 30 minutes should be spent on elliptical trainer and 10 minutes on stationary bike.

Explanation of Solution

Given:

There are 40 minutes to exercise

Need to burn 300 calories

Calculation:

Let $e$ be the time spent on elliptical trainer and $s$ be the time spend on stationary bike. $\begin{array}{r}\hfill e+s=40\\ \hfill 8e+6s=300\end{array}$

Rearranging,

  $s=40-e$

  $s=\frac{300-8s}{6}$

The first equation for the relevant values is plotted in red colour and the second equation in blue colour.

  

In graph, it seems that (30,10) is solution of system of equations. Check if it is indeed the solution.

  $\begin{array}{r}\hfill e+s=40\\ \hfill 30+10=40\\ \hfill 40=40\\ \hfill 8e+6s=300\\ \hfill 8(30)+6(10)=300\\ \hfill 240+60=300\\ \hfill 300=300\end{array}$

As the point satisfies both equations, it is solution of system of equations.

Thus, 30 minutes should be spent on elliptical trainer and 10 minutes on stationary bike.

Conclusion:

Thus, 30 minutes should be spent on elliptical trainer and 10 minutes on stationary bike.