Chapter 5.7, Problem 36E

To determine

The hours that you and your friend each drive in 1 day.

Answer to Problem 36E

You spend 4 hours driving & your friend spend 10 hours

Explanation of Solution

Given information:

On a road trip with the friend, the drive is about 70 miles per second and your friend drives 60 miles per second. The plan is to drive less than 15 hours and at least 600 miles each day.

Formula used:

The graph represents x axis which is horizontal axis and y represents vertical axis.

Calculation:

Let:

  $\begin{array}{l}x\to \text{amount of time you can drive}\\ y\to \text{amount of time your friend can drive}\end{array}$

Set up the inequalities:

Drive less than 15 hours

  $x+y<15$

At least 600 miles a day

  $70x+60y\ge 600$

Your friend drives more hours

  $y>x$

Graph the equations:

  $\begin{array}{l}x+y=15\\ y=-x+15\left(\text{shade}\text{lower}\text{half}\right)\\ 70x+60y=600\\ y=-\frac{7}{6}x+10\left(\text{shade upper half}\right)\end{array}$

  $y=x$ (Shade upper half)

Restrict the graph to positive x & y values since negative values do not make sense in this real- life context

The solution is the intersection (yellow shaded area):

  

A possible solution is:

(4, 10) $\to$ you spend 4 hours driving & your friend spend 10 hours

Conclusion:

You spend 4 hours driving & your friend spend 10 hours