Chapter 6.6, Problem 1MP

(a)

To determine

To determine an inequality representing the condition:

Miguel will spend at most 60 minutes working out at the gym

Answer to Problem 1MP

  $x+y\le 60$

Explanation of Solution

Given information:

Let x represents the number of minutes Miguel spends on the stair machine and y represents the number of minutes Miguel spends on the rowing machine.

Since, it is given that Miguel spend at most 60 minutes at the the gym,

sum of the number of minutes Miguel spends on the stair machine and rowing machine

will be maximum 60 minutes.

That is, $x+y\le 60$

(b)

To determine

To determine an inequality representing the condition:

Miguel will exercise for at least 30 minutes.

Answer to Problem 1MP

  $x+y\ge 30$

Explanation of Solution

Given information:

Let x represents the number of minutes Miguel spends on the stair machine and y represents the number of minutes Miguel spends on the rowing machine.

Since, it is given that Miguel will exercise at least 30 minutes at the the gym,

sum of the number of minutes Miguel spends on the stair machine and rowing machine

will be minimum 30 minutes.

That is, $x+y\ge 30$

(c)

To determine

To determine an inequality representing the condition:

Miguel will spend at least twice as much as time on the stair machine as on the rowing machine.

Answer to Problem 1MP

  $2y\le x$

Explanation of Solution

Given information:

Let x represents the number of minutes Miguel spends on the stair machine and y represents the number of minutes Miguel spends on the rowing machine.

Since, it is given that Miguel will spend at least twice as much as time on the stair machine as on the rowing machine, which means that the time Miguel spend on stair machine should not be less than the time spend on rowing machine. Also the time Miguel spend on stair machine should be double the time spend on rowing machine.

  $\Rightarrow x=2y$ or x not less than y

  $\Rightarrow$$x\ge 2y$

∴ $2y\le x$