A car is traveling at a constant speed of miles per hour. What is this speed in feet per second? (Use the relationship mile feet.)

Solution available with step-by-step explanation

SAT Ratios, Rates & Proportions Question 44 | Free SAT Prep | Aniko

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Question 44·Medium·Ratios, Rates, Proportional Relationships, and Units

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A car is traveling at a constant speed of $45$ miles per hour. What is this speed in feet per second?

(Use the relationship $1$ mile $= 5,280$ feet.)

Your answer

(Express the answer as an integer)

For unit-conversion questions, always write the given rate as a fraction and then multiply by conversion fractions that equal 1 (like $\frac{5280\,\text{feet}}{1\,\text{mile}}$ and $\frac{1\,\text{hour}}{3600\,\text{seconds}}$ ), arranging them so unwanted units cancel. After the units are set up correctly, combine the numbers step by step, simplifying fractions or canceling zeros to keep the arithmetic quick and accurate.

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Think about unit cancellation

Start by writing $45$ miles per hour as a fraction and then multiply by conversion fractions so that the units you don't want (miles and hours) cancel out, leaving feet per second.

Use the miles-to-feet conversion first

Use $1$ mile $= 5280$ feet to replace miles with feet. What do you multiply $45$ miles per hour by so that "mile" cancels?

Don’t forget to convert hours to seconds

After you have feet per hour, remember that $1$ hour $= 3600$ seconds. How can you use this fact to turn "per hour" into "per second"?

Combine the numbers carefully

Once your setup is $45 \times 5280 \div 3600$ , multiply the first two numbers, then divide by the last one. Be careful with large-number arithmetic or use step-by-step simplification (like canceling zeros) to make it easier.

Desmos Guide

Compute the conversion directly

In Desmos, type the expression 45*5280/3600. The numerical value that Desmos outputs is the speed in feet per second.

Step-by-step Explanation

Set up the unit conversion

We want to change $45$ miles per hour into feet per second.

Write it as a chain of conversions so units cancel:

45 \;\frac{\text{miles}}{\text{hour}} \times \frac{5280\;\text{feet}}{1\;\text{mile}} \times \frac{1\;\text{hour}}{3600\;\text{seconds}}

Check that:

"miles" cancels with "miles"
"hours" cancels with "hours"

The final unit left is feet per second, which is what we want.

Convert miles to feet

First, multiply $45$ by $5280$ to change miles to feet while still being per hour:

45 \times 5280 = 237{,}600

So now the speed is:

237{,}600 \;\frac{\text{feet}}{\text{hour}}

Next, convert hours in the denominator to seconds.

Convert hours to seconds and simplify

There are $3600$ seconds in $1$ hour, so divide by $3600$ to change per hour to per second:

\frac{237{,}600\;\text{feet/hour}}{3600\;\text{seconds/hour}} = \frac{237{,}600}{3600}\;\frac{\text{feet}}{\text{second}}

Simplify the fraction:

\frac{237{,}600}{3600} = \frac{2376}{36} = 66

So the car's speed is $66$ feet per second.

Strategy

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Step-by-step Explanation

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Strategy

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Desmos Guide

Step-by-step Explanation