Chapter 3.6, Problem 33E

To determine

To calculate:The minimum amount of time one should spend swimming the breaststroke.

Answer to Problem 33E

The answer is 10 minutes. One should spend minimum 10 minutes swimming breaststroke to burn at least 300 calories.

Explanation of Solution

Given information:The minimum number of calories that one wants to burn is given $=300$ .

The number of calories one burns per minute of swimming breaststroke is given $=12.$

The number of calories one burns per minute of swimming backstroke is given $=9.$

The maximum time is given = 30 minutes.

Formula used:The concept of solving multi-step inequalities is to be used.

Calculation:

Let $x$ represent the number of minutes one spent swimming breaststroke.

Let $y$ represent the number of minutes one spent swimming breaststroke.

We know that on swimming 1 minute breaststroke, one burns 12 calories. Similarly, on swimming 1 minute backstroke, one burns 9 calories.

So the total number of calories burnt are,

  $\Rightarrow 12\times x+9\times y$

The minimum calories that must be burnt is 300.

  $\Rightarrow 12x+9y\ge 300$ - (1)

The maximum time is 30 minutes.

  $\Rightarrow x+y\le 30$ - (2)

Solve Equations (1) and (2),

Multiply Equation (2) with 9,

  $\Rightarrow 9x+9y\le 270$ - (3)

Subtract Equation (3) from Equation (1)

  $\Rightarrow \text{ 12}x+9y-(9x+9y)\le 300-270$

  $\begin{array}{l}\Rightarrow 3x\le 30\\ \Rightarrow x\le 10\end{array}$

Thus, the minimum minutes one has to swim in breaststroke to burn minimum 300 calories is 10 minutes.