Chapter 5.4, Problem 47HP

To determine

To find:The rate that does not belong to the other three given rates.

Answer to Problem 47HP

The rate that does not belong to the other three given rates is $500\frac{\text{ft}}{\text{min}}$ .

Explanation of Solution

Given information:

Thefour different rates are $60\frac{\text{mi}}{\text{h}}$ , $88\frac{\text{ft}}{\text{s}}$ , $500\frac{\text{ft}}{\text{min}}$ and $1440\frac{\text{mi}}{\text{day}}$ .

Calculation:

To find the same value of the rate, convert each rate to miles per hour.

The conversion offeet per second into miles per second is:

  $1\frac{\text{ft}}{\text{s}}=\frac{1}{5280}\text{}\frac{\text{mi}}{\text{s}}$

To find the conversion of $88\frac{\text{ft}}{\text{s}}$ ,multiply both sides of above conversion by $88$ .

  $\begin{array}{c}88\times 1\frac{\text{ft}}{\text{s}}=88\times \frac{1}{5280}\text{}\frac{\text{mi}}{\text{s}}\\ =\frac{88}{5280}\text{}\text{}\frac{\text{mi}}{\text{s}}\\ =0.01667\text{}\frac{\text{mi}}{\text{s}}\end{array}$

The conversion of mile per second into miles per hour is:

  $1\frac{\text{mi}}{\text{s}}=\frac{3600}{1}\text{}\frac{\text{mi}}{\text{h}}$

To find the conversion of $0.01667\text{}\frac{\text{mi}}{\text{s}}$ , multiply both sides of above conversion by $0.01667\text{}$ .

  $\begin{array}{c}0.01667\times 1\frac{\text{mi}}{\text{s}}=0.01667\times \frac{3600}{1}\text{}\frac{\text{mi}}{\text{h}}\\ =60.012\text{}\frac{\text{mi}}{\text{h}}\\ \approx 60\text{}\frac{\text{mi}}{\text{h}}\end{array}$

Therefore, the conversion of $88\frac{\text{ft}}{\text{s}}$ into miles per houris $60\frac{\text{mi}}{\text{h}}$ .

The conversion offeet per minute into miles per minute is:

  $1\frac{\text{ft}}{\text{min}}=\frac{1}{5280}\text{}\frac{\text{mi}}{\text{min}}$

To find the conversion of $500\frac{\text{ft}}{\text{min}}$ , multiply both sides of above conversion by $500$ .

  $\begin{array}{c}500\times 1\frac{\text{ft}}{\min }=500\times \frac{1}{5280}\text{}\frac{\text{mi}}{\min }\\ =\frac{500}{5280}\text{}\text{}\frac{\text{mi}}{\text{min}}\\ =0.0947\text{}\frac{\text{mi}}{\text{min}}\end{array}$

The conversion of mile per minute into miles per hour is:

  $1\text{}\frac{\text{mi}}{\text{min}}=\frac{60}{1}\text{}\frac{\text{mi}}{\text{h}}$

To find the conversion of $0.0947\text{}\frac{\text{mi}}{\text{min}}$ , multiply both sides of above conversion by $0.0947$ .

  $\begin{array}{c}0.0947\times 1\text{}\frac{\text{mi}}{\text{min}}=0.0947\times \frac{60}{1}\text{}\frac{\text{mi}}{\text{h}}\\ =5.682\text{}\frac{\text{mi}}{\text{h}}\end{array}$

Therefore, the conversion of $500\frac{\text{ft}}{\text{min}}$ into miles per hour is $5.682\text{}\frac{\text{mi}}{\text{h}}$ .

The conversion of miles per day into miles per hour is:

  $1\frac{\text{mi}}{\text{day}}=\frac{1}{24}\text{}\frac{\text{mi}}{\text{h}}$

To find the conversion of $1440\frac{\text{mi}}{\text{day}}$ , multiply both sides of above conversion by $1440$ .

  $\begin{array}{c}1440\times 1\frac{\text{mi}}{\text{day}}=1440\times \frac{1}{24}\text{}\frac{\text{mi}}{\text{h}}\\ =\frac{60}{1}\frac{\text{mi}}{\text{h}}\end{array}$

Therefore, the conversion of $1440\frac{\text{mi}}{\text{day}}$ into meters per hour is $360\text{meters}\text{per}\text{hour}$ .

Therefore, the rate $500\frac{\text{ft}}{\text{min}}$ does not belong to the other three given rates.