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9.8: Speedo

Difficulty Level: At Grade Created by: CK-12
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Speedo – Use Formulas

Teacher Notes

Students apply the \begin{align*}\text{distance} = \text{rate} \times \text{time} \ (D = rt)\end{align*} formula to the solution of problems involving average speeds. For some problems, students will convert feet to miles \begin{align*}(1 \ mile = 5280 \ feet)\end{align*} and seconds to minutes to hours. Encourage students to use calculators for the “messy” calculations.

Solutions

Speedo 1

\begin{align*}D = rt\\ D = 264 \ ft/sec \times 0.5 \ sec\\ D = 132 \ ft\end{align*}

Speedo 2

\begin{align*}D = rt\\ 5000 \ ft = 200 \ ft/sec \times t\\ \frac{5000 \ ft}{200 \ ft/sec} = t\\ 25 \ seconds = t\end{align*}

Speedo 3

\begin{align*}D = rt\\ \frac{1}{2} \ mile = \frac{5280}{2}, \ \text{or} \ 2640 \ ft\\ 2640 = 37.9 \ ft/sec \times t\\ \frac{2640}{37.9} = t\\ 69.7 \ sec = t\\ t \ \text{is about} \ 1 \ \text{minute}.\end{align*}

The average speed of the winner in the 30-minute bicycle race was 52 feet per second. To the nearest tenth of a mile, how many miles was the race?

\begin{align*}&\mathbf{Describe:}&& \text{Speed is 52 feet per second}.\\ &&& \text{Time is 30 minutes}.\\ \\ &\mathbf{My \ Job:}&& \text{Figure out the length of the race in miles}.\\ \\ &\mathbf{Plan:} && \text{Speed is another name for rate. Since time is in minutes, figure out the rate}\\ &&& \text{in minutes. Replace} \ t \ \text{and} \ r \ \text{with their values in the formula,} \ D = rt. \ \text{Solve}\\ &&&\text{for} \ D \ \text{in feet. Divide the number of feet by} \ 5280 \ \text{to get the number of}\\ &&&\text{miles}.\\ \\ &\mathbf{Solve:}&& \text{Rate:} \ 52 \ feet/second \ \text{is} \ 52 \times 60 \ seconds/minute, \ \text{or} \ 3120 \ feet/minute.\\ &&& D = rt\\ &&& D = 3120 \ ft/min \times 30 \ min, \ \text{or} \ 93,600 \ ft\\ &&& D = \frac{93,600}{5280 \ ft/mile}\\ &&& D = 17.7 \ miles\\ &&& \text{The race was} \ 17.7 \ miles \ \text{long.}\\ \\ &\mathbf{Check:} && 3120 \ ft/min \ \text{is} \ \frac{3120}{5280}, \ \text{or} \ 0.59 \ miles/min\\ &&&\text{In} \ 30 \ minutes, \ \text{the biker will cover} \ 30 \times 0.59 \ miles, \ \text{or} \ 17.7 \ miles.\end{align*}

Use the \begin{align*}\textbf{D = \textit{rt}}\end{align*} formula.

Solve these problems.

Show the steps.

\begin{align*}1. \quad \text{The fastest moving ball in any game is the pelota in the game of Jai-Alai. In one game the}\!\\ {\;} \quad \ \text{pelota was clocked at 264 feet per second. At that speed, how far will the pelota travel in 0.5}\!\\ {\;} \quad \ \text{seconds?}\!\\ \\ \\ \\ \\ 2. \quad \text{A sky diver in free fall sometimes reaches a speed of 200 feet per second. At that speed, how}\!\\ {\;} \quad \ \text{long would it take a sky diver to descend 5000 feet?}\!\\ \\ \\ \\ \\ 3. \quad \text{One of the record speeds for a roller skater is 37.9 feet per second. At this speed, about how}\!\\ {\;} \quad \ \text{many minutes would it take to skate} \ \frac{1}{2} \ \text{mile?}\end{align*}

Extra for Experts: Speedo – Use Formulas

Solutions

Extra for Experts, Speedo 1

\begin{align*}D= rt\\ 100 \ yards = 300 \ ft\\ 300 \ ft = 6.65 \ ft/sec \times \textbf{\textit{t}}\\ 300 \ ft/6.65 \ ft/sec = \textbf{\textit{t}}\\ \textbf{\textit{t}} \ \text{is about 45 seconds.}\end{align*}

Extra for Experts, Speedo 2

\begin{align*}D= rt\\ 9 \ ft = \textbf{\textit{r}} \times 0.075 \ sec\\ 9 \ ft/0.075 \ sec = \textbf{\textit{r}}\\ 120 \ ft/sec = \textbf{\textit{r}}\end{align*}

Extra for Experts, Speedo 3

\begin{align*}D= rt\\ 59 \ ft = \textbf{\textit{r}} \times 0.3 \ sec\\ 59 \ ft/0.3 \ sec = \textbf{\textit{r}}\\ 196.7 \ ft/sec = \textbf{\textit{r}}\end{align*}

Extra for Experts: Speedo – Use Formulas

Use the \begin{align*}\textbf{D= \textit{rt}}\end{align*} formula.

Solve these problems.

Show the steps.

\begin{align*}1. \quad \text{One of the fastest swimmers swam 100 yards at the rate of 6.65 feet per second. How long}\!\\ {\;} \quad \ \text{did it take the swimmer to swim the 100 yards?}\!\\ \\ \\ \\ \\ 2. \quad \text{A hard hit table tennis ball can travel the length of the 9 foot table in 0.075 second. At that}\!\\ {\;} \quad \ \text{speed, how far would the table tennis ball travel in one second?}\!\\ \\ \\ \\ \\ 3. \quad \text{In 0.3 second, a well hit volley ball can travel 59 feet, the length of a volley ball court. How}\!\\ {\;} \quad \ \text{far could a hard hit volleyball travel in one second?}\end{align*}

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CK.MAT.ENG.SE.1.Algebra-Explorations-K-7.9.8
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