Rate and Unit Word Problems - SSAT Upper Level Quantitative

If apples cost $6 for $4$ lb, what is the unit price in $\$/\text{lb}$ ?

$\$1.50/\text{lb}$ . Divide total cost by weight in pounds to determine the price per pound.
State the unit conversion for $1$ kilometer in meters.

$1\text{ km}=1000\text{ m}$ . Metric length conversion where one kilometer equals one thousand meters.
State the unit conversion for $1$ foot in inches.

$1\text{ ft}=12\text{ in}$ . Imperial length conversion where one foot equals twelve inches.
State the unit conversion for $1$ meter in centimeters.

$1\text{ m}=100\text{ cm}$ . Metric length conversion where one meter equals one hundred centimeters.
A cyclist rides $18$ km in $45$ min. What is the speed in km/h?

$24\text{ km/h}$ . Divide distance by time in hours (converting minutes to hours) to find speed.
A car uses $9$ gallons to go $270$ miles. What is the fuel efficiency in mpg?

$30\text{ mpg}$ . Divide miles traveled by gallons used to compute miles per gallon.
If a machine makes $12$ parts in $4$ minutes, how many parts does it make in $15$ minutes?

$45\text{ parts}$ . Determine rate per minute, then multiply by total time to find parts produced.
A tank holds $60$ gallons and drains at $5\text{ gal/min}$ . How long to empty it?

$12\text{ min}$ . Divide tank capacity by drainage rate to find time to empty in minutes.
Find the distance traveled at $12\text{ m/s}$ for $15\text{ s}$ .

$180\text{ m}$ . Multiply speed in meters per second by time in seconds to find distance in meters.
Identify the unit rate: $150$ miles in $3$ hours equals how many mph?

$50\text{ mph}$ . Divide total distance by time to compute the average rate in miles per hour.
State the unit conversion for $1$ pound in ounces.

$1\text{ lb}=16\text{ oz}$ . Imperial weight conversion where one pound equals sixteen ounces.
State the unit conversion for $1$ hour in minutes.

$1\text{ hr}=60\text{ min}$ . Standard time conversion where one hour equals sixty minutes.
A printer makes $24$ pages in $3$ minutes. What is the rate in pages per minute?

$8\text{ pages/min}$ . Divide total pages by time in minutes to find the printing rate.
State the formula relating distance, rate, and time.

$d=rt$ . This formula calculates distance as the product of constant rate and time elapsed.
A runner completes $6$ miles in $48$ minutes. What is the pace in minutes per mile?

$8\text{ min/mi}$ . Divide total time by distance to find pace in minutes per mile.
State the unit conversion for $1$ minute in seconds.

$1\text{ min}=60\text{ s}$ . Standard time conversion where one minute equals sixty seconds.
State the unit conversion for $1$ mile in feet.

$1\text{ mi}=5280\text{ ft}$ . Imperial length conversion where one mile equals five thousand two hundred eighty feet.
Find the time needed to travel $120$ miles at $40\text{ mph}$ .

$3\text{ hr}$ . Divide distance in miles by rate in miles per hour to find time in hours.
State the unit conversion for $1$ gallon in quarts.

$1\text{ gal}=4\text{ qt}$ . Imperial volume conversion where one gallon equals four quarts.
State the unit conversion for $1$ yard in feet.

$1\text{ yd}=3\text{ ft}$ . Imperial length conversion where one yard equals three feet.
Convert a speed of $90\text{ mph}$ to miles per minute.

$1.5\text{ mi/min}$ . Divide miles per hour by sixty to convert to miles per minute.
A recipe uses $\frac{3}{4}$ cup sugar per batch. How many cups for $6$ batches?

$\frac{9}{2}\text{ cups}$ . Multiply sugar per batch by number of batches to find total cups needed.
Two machines make parts at $5$ parts/min and $7$ parts/min. What is the combined rate?

$12\text{ parts/min}$ . Add individual rates of machines working together to find combined production rate.
Convert a speed of $3\text{ mi/min}$ to miles per hour.

$180\text{ mph}$ . Multiply miles per minute by sixty to convert to miles per hour.
A map scale is $1$ inch : $20$ miles. How many miles does $3.5$ inches represent?

$70\text{ miles}$ . Multiply map distance by scale ratio to convert to actual miles.

Study these flashcards