Chapter 5.7, Problem 23IP

To determine

To find: The distance would the boat travel in $1\text{minute}$ and in 1 minute 30 seconds.

Answer to Problem 23IP

The distance would the boat travel in $1\text{minute}$ is $927.6\text{feet}$ and in 1 minute 30 seconds is $1391.4\text{feet}$ .

Explanation of Solution

Given information:

The distance travelled by boat in $9.7\text{seconds}$ is $150\text{feet}$ .

Calculation:

The constant of proportionality for each feet distance travelled by boat is,

  $\begin{array}{c}\frac{\text{Distance}\text{in feet}}{\text{Time in seconds}}=\frac{150}{9.7}\\ =15.46\end{array}$

Hence, $15.46\text{feet}$ of distance covered in each second.

Let $x$ be the distance travelled by boat and $y$ be the time required.

Thedistance would the boat travel is calculated as,

  $x=15.46y$.........................(1)

The time unit from minute into seconds is converted as,

  $1\text{minute}=60\text{seconds}$

Hence, 1 minute 30 seconds is converted in seconds as,

  $\begin{array}{c}1\text{minute 30 seconds}=60+30\text{seconds}\\ =\text{90}\text{seconds}\end{array}$

Substitute $60$ for $y$ to calculate the distance travelled by boat in $1\text{minute}$ to the equation (1).

  $\begin{array}{c}x=15.46y\\ =15.46\times 60\\ =927.6\text{feet}\end{array}$

Substitute $90$ for $y$ to calculate the distance travelled by boat in 1 minute 30 seconds to the equation (1).

  $\begin{array}{c}x=15.46y\\ =15.46\times 90\\ =1391.4\text{feet}\end{array}$

Therefore, the distance would the boat travel in $1\text{minute}$ is $927.6\text{feet}$ and in 1 minute 30 seconds is $1391.4\text{feet}$ .