Chapter 6.6, Problem 27PPE

To determine

To determine a graph showing how they can split the driving each day.

Explanation of Solution

Given:

One friend drives at an average speed of 60 miles/hour

Other friend drives at an average speed of 55 miles/hour

Drive at least 500 miles per day

Plan to spend no more than 10 hours driving each day

Calculation:

Let’s consider $x=$ time of driving at an average speed of 60 miles/hour, $y=$ time of driving at an average speed of 55 miles/hour.

The minimum driving per day 500 miles.

So the equation is,

  $\Rightarrow 60x+55y\ge 500$

Plan to spend no more than 10 hours driving each day,

So equation representation is,

  $\Rightarrow x+y\le 10$

Slower driver drives few hours:

  $\Rightarrow y<x$

Graph:

  

The purple line and below it represents $\Rightarrow x+y\le 10$

The green line and above it represents $\Rightarrow 60x+55y\ge 500$

The yellow line and below it represents $\Rightarrow y<x$

Interpretation:

Therefore, the graph showing how they can split the driving each day.