Question 1·Easy·Ratios, Rates, Proportional Relationships, and Units
A car travels at a constant speed of miles per hour. What is this speed, in feet per second? (Use feet mile and seconds hour.)
(Express the answer as an integer)
For unit-conversion questions, always write the given rate as a fraction with units (like ), then multiply by conversion factors written as fractions that equal 1 (such as and ), making sure unwanted units cancel. Once the units are correct, simplify the resulting fraction carefully, canceling zeros and reducing in steps to avoid arithmetic mistakes. This “unit-canceling” approach is fast, organized, and greatly reduces errors on SAT rate problems.
Hints
Focus on the units
Rewrite 15 miles per hour as the fraction . What units do you want in the final answer?
Change miles into feet first
Use feet mile. What can you multiply by so that the mile units cancel and you get feet on top?
Now change hours into seconds
After you have feet per hour, use seconds hour to turn hours into seconds. Make sure the hour units cancel and check whether you should multiply or divide by .
Simplify carefully
You should end up with a fraction like . Try canceling zeros first, then reduce the smaller numbers step by step.
Desmos Guide
Use Desmos to check the unit conversion
In a new expression line, type (15*5280)/3600. The value that Desmos displays is the car’s speed in feet per second.
Step-by-step Explanation
Write the speed as a rate with units
The car’s speed is miles per hour, which we can write as the fraction
We want to change this to feet per second: .
Convert miles to feet
Use feet mile to replace miles with feet.
Multiply by a conversion factor that equals 1:
The “miles” units cancel, leaving
So the speed is feet per hour.
Convert hours to seconds
Now convert hours to seconds using seconds hour.
To get feet per second, we need seconds in the denominator, so we divide by seconds per hour:
Now the unit is feet per second, as desired.
Simplify the fraction to get the final speed
Simplify
First, cancel two zeros from top and bottom:
Now divide both numerator and denominator by 4:
Then divide by :
So the car’s speed is feet per second, and the correct answer is .