Question 1·Easy·Problem Solving and Data Analysis

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A car travels at a constant speed of $15$ miles per hour. What is this speed, in feet per second? (Use $5{,}280$ feet $=1$ mile and $3{,}600$ seconds $=1$ hour.)

Your answer

A speed given in miles per hour but requested in feet per second calls for unit conversion on both sides of the rate. Write “per” as a fraction bar, then choose conversion factors that cancel miles and hours. Once only feet per second remains, type the numbers into Desmos. The main trap is converting miles but not hours.

Hints

Hint 1
A conversion factor is a fraction whose top and bottom describe the same amount. Miles start on top of the speed fraction, so where should miles go in the feet-to-miles factor to cancel?
Hint 2
In a rate, “per hour” puts hours on the bottom. To cancel hours, put hours on top of the next conversion factor. Where will seconds go so the result is feet per second?

Step-by-step

Cancel units, then calculate
Step 1
Convert miles to feet
“Per hour” means divided by hours. The given $5{,}280$ feet and $1$ mile are the same distance, so their ratio is a conversion factor equal to $1$ . Put miles on the bottom to cancel miles on top:
$15\frac{\text{miles}}{\text{hour}}\left(\frac{5{,}280\text{ feet}}{1\text{ mile}}\right)\quad\longrightarrow\quad\frac{\text{feet}}{\text{hour}}.$
Step 2
Convert hours to seconds
Hours are on the bottom of the rate, so put $1$ hour on top of the next factor. The equivalent $3{,}600$ seconds go below it: $15\frac{\text{miles}}{\text{hour}}\left(\frac{5{,}280\text{ feet}}{1\text{ mile}}\right)\left(\frac{1\text{ hour}}{3{,}600\text{ seconds}}\right)\quad\longrightarrow\quad\frac{\text{feet}}{\text{second}}$ . In a speed conversion, both the distance unit and the time unit must cancel. Putting seconds on top instead would leave hours on the bottom.
Step 3
Calculate the speed
The units are settled, so type $15\cdot5{,}280/3{,}600$ into Desmos. It shows $22$ . That means the car travels 22 feet per second. Grid in 22.

Question 1·Easy·Problem Solving and Data Analysis

Strategy

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