Rates - PSAT Math
Card 1 of 30
What is the time needed to travel $150$ miles at $50$ miles per hour?
What is the time needed to travel $150$ miles at $50$ miles per hour?
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$3$ hours. Using $t = \frac{d}{r}$: $\frac{150}{50} = 3$ hours.
$3$ hours. Using $t = \frac{d}{r}$: $\frac{150}{50} = 3$ hours.
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Identify the unit rate: $15$ miles in $\frac{1}{2}$ hour equals how many miles per hour?
Identify the unit rate: $15$ miles in $\frac{1}{2}$ hour equals how many miles per hour?
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$30$ miles per hour. $15 \div \frac{1}{2} = 15 \times 2 = 30$ miles per hour.
$30$ miles per hour. $15 \div \frac{1}{2} = 15 \times 2 = 30$ miles per hour.
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What is the formula for density given mass $m$ and volume $V$, with $V \ne 0$?
What is the formula for density given mass $m$ and volume $V$, with $V \ne 0$?
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$\rho = \frac{m}{V}$. Density equals mass divided by volume.
$\rho = \frac{m}{V}$. Density equals mass divided by volume.
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What is the formula for speed given distance $d$ traveled in time $t$, with $t \ne 0$?
What is the formula for speed given distance $d$ traveled in time $t$, with $t \ne 0$?
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$r = \frac{d}{t}$. Rate equals distance divided by time.
$r = \frac{d}{t}$. Rate equals distance divided by time.
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What is the formula for price per unit if total cost is $C$ for $n$ items, with $n \ne 0$?
What is the formula for price per unit if total cost is $C$ for $n$ items, with $n \ne 0$?
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$\frac{C}{n}$ dollars per item. Unit price equals total cost divided by quantity.
$\frac{C}{n}$ dollars per item. Unit price equals total cost divided by quantity.
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What is the combined work rate if one job takes $a$ hours and another takes $b$ hours?
What is the combined work rate if one job takes $a$ hours and another takes $b$ hours?
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$\frac{1}{a} + \frac{1}{b}$ jobs per hour. Combined rate is sum of individual rates $\frac{1}{a}$ and $\frac{1}{b}$.
$\frac{1}{a} + \frac{1}{b}$ jobs per hour. Combined rate is sum of individual rates $\frac{1}{a}$ and $\frac{1}{b}$.
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What is the time to finish $1$ job at constant work rate $r$ jobs per hour, with $r \ne 0$?
What is the time to finish $1$ job at constant work rate $r$ jobs per hour, with $r \ne 0$?
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$\frac{1}{r}$ hours. Time is reciprocal of rate for one job.
$\frac{1}{r}$ hours. Time is reciprocal of rate for one job.
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What is the formula for time given distance $d$ at constant speed $r$, with $r \ne 0$?
What is the formula for time given distance $d$ at constant speed $r$, with $r \ne 0$?
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$t = \frac{d}{r}$. Time equals distance divided by rate.
$t = \frac{d}{r}$. Time equals distance divided by rate.
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What is the average speed formula for total distance $D$ over total time $T$, with $T \ne 0$?
What is the average speed formula for total distance $D$ over total time $T$, with $T \ne 0$?
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$\text{avg speed} = \frac{D}{T}$. Average speed is total distance over total time.
$\text{avg speed} = \frac{D}{T}$. Average speed is total distance over total time.
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What is the unit rate for a rate of $\frac{a}{b}$ units per unit, with $b \ne 0$?
What is the unit rate for a rate of $\frac{a}{b}$ units per unit, with $b \ne 0$?
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$\frac{a}{b}$ per $1$ unit. Divide the rate by the denominator to get the unit rate.
$\frac{a}{b}$ per $1$ unit. Divide the rate by the denominator to get the unit rate.
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What is the miles-per-gallon formula if you drive $m$ miles using $g$ gallons, with $g \ne 0$?
What is the miles-per-gallon formula if you drive $m$ miles using $g$ gallons, with $g \ne 0$?
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$\frac{m}{g}$ miles per gallon. Fuel efficiency equals miles divided by gallons.
$\frac{m}{g}$ miles per gallon. Fuel efficiency equals miles divided by gallons.
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What is the formula for distance when traveling at constant speed $r$ for time $t$?
What is the formula for distance when traveling at constant speed $r$ for time $t$?
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$d = rt$. Distance equals rate times time for constant motion.
$d = rt$. Distance equals rate times time for constant motion.
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What is the flow rate in gallons per minute if $8$ gallons fill in $40$ seconds?
What is the flow rate in gallons per minute if $8$ gallons fill in $40$ seconds?
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$12$ gallons per minute. $8$ gallons in $\frac{40}{60}$ minutes = $8 \div \frac{2}{3} = 12$ gal/min.
$12$ gallons per minute. $8$ gallons in $\frac{40}{60}$ minutes = $8 \div \frac{2}{3} = 12$ gal/min.
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What is the speed if you travel $45$ miles in $\frac{3}{4}$ hour?
What is the speed if you travel $45$ miles in $\frac{3}{4}$ hour?
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$60$ miles per hour. Using $r = \frac{d}{t}$: $\frac{45}{\frac{3}{4}} = 45 \times \frac{4}{3} = 60$ mph.
$60$ miles per hour. Using $r = \frac{d}{t}$: $\frac{45}{\frac{3}{4}} = 45 \times \frac{4}{3} = 60$ mph.
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What is the combined work time if one worker takes $6$ hours and another takes $3$ hours?
What is the combined work time if one worker takes $6$ hours and another takes $3$ hours?
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$2$ hours. Combined rate $\frac{1}{6} + \frac{1}{3} = \frac{1}{2}$, so time is $2$ hours.
$2$ hours. Combined rate $\frac{1}{6} + \frac{1}{3} = \frac{1}{2}$, so time is $2$ hours.
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What is the combined work rate if one job takes $4$ hours and another takes $12$ hours?
What is the combined work rate if one job takes $4$ hours and another takes $12$ hours?
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$\frac{1}{3}$ jobs per hour. $\frac{1}{4} + \frac{1}{12} = \frac{3}{12} + \frac{1}{12} = \frac{4}{12} = \frac{1}{3}$.
$\frac{1}{3}$ jobs per hour. $\frac{1}{4} + \frac{1}{12} = \frac{3}{12} + \frac{1}{12} = \frac{4}{12} = \frac{1}{3}$.
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What is the cost per ounce if $12$ ounces cost $\$3$?
What is the cost per ounce if $12$ ounces cost $\$3$?
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$\$0.25$ per ounce. $$3 \div 12 = $0.25$ per ounce.
$\$0.25$ per ounce. $$3 \div 12 = $0.25$ per ounce.
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What is the unit price per pound if $\frac{3}{2}$ pounds cost $\$6$?
What is the unit price per pound if $\frac{3}{2}$ pounds cost $\$6$?
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$\$4$ per pound. $$6 \div \frac{3}{2} = $6 \times \frac{2}{3} = $4$ per pound.
$\$4$ per pound. $$6 \div \frac{3}{2} = $6 \times \frac{2}{3} = $4$ per pound.
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What is the average speed for $120$ miles in $2$ hours, then $60$ miles in $1$ hour?
What is the average speed for $120$ miles in $2$ hours, then $60$ miles in $1$ hour?
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$60$ miles per hour. Total: $180$ miles in $3$ hours = $60$ mph average.
$60$ miles per hour. Total: $180$ miles in $3$ hours = $60$ mph average.
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How long to make $1$ item together if A makes $1$ item in $6$ min and B makes $1$ item in $3$ min?
How long to make $1$ item together if A makes $1$ item in $6$ min and B makes $1$ item in $3$ min?
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$2\text{ minutes}$. Reciprocal of combined rate: $\frac{1}{\frac{1}{2}} = 2$ minutes.
$2\text{ minutes}$. Reciprocal of combined rate: $\frac{1}{\frac{1}{2}} = 2$ minutes.
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What is the cost of $7$ pounds at $\$2.40$ per pound?
What is the cost of $7$ pounds at $\$2.40$ per pound?
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$\$16.80$. $7 \times 2.40 = 16.80$ dollars.
$\$16.80$. $7 \times 2.40 = 16.80$ dollars.
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What is the interest formula for simple interest with principal $P$, rate $r$, time $t$?
What is the interest formula for simple interest with principal $P$, rate $r$, time $t$?
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$I=Prt$. Interest equals principal times rate times time.
$I=Prt$. Interest equals principal times rate times time.
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What is the total amount formula for simple interest with principal $P$, rate $r$, time $t$?
What is the total amount formula for simple interest with principal $P$, rate $r$, time $t$?
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$A=P+Prt$. Total equals principal plus interest earned.
$A=P+Prt$. Total equals principal plus interest earned.
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Identify the unit rate: A car travels $150$ miles in $3$ hours. What is the speed?
Identify the unit rate: A car travels $150$ miles in $3$ hours. What is the speed?
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$50$ miles per hour. Divide total distance by total time: $ rac{150}{3}=50$.
$50$ miles per hour. Divide total distance by total time: $ rac{150}{3}=50$.
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Identify the unit price: $12$ apples cost $\$6$. What is the cost per apple?
Identify the unit price: $12$ apples cost $\$6$. What is the cost per apple?
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$\$0.50$ per apple. Divide total cost by quantity: $ rac{$6}{12}=$0.50$.
$\$0.50$ per apple. Divide total cost by quantity: $ rac{$6}{12}=$0.50$.
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Find the time: A runner goes $9$ miles at $6$ miles per hour. How long does it take?
Find the time: A runner goes $9$ miles at $6$ miles per hour. How long does it take?
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$1.5$ hours. Use $t= rac{d}{s}$: $ rac{9}{6}=1.5$ hours.
$1.5$ hours. Use $t= rac{d}{s}$: $ rac{9}{6}=1.5$ hours.
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Find the distance: A cyclist rides at $12$ miles per hour for $2.5$ hours. How far?
Find the distance: A cyclist rides at $12$ miles per hour for $2.5$ hours. How far?
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$30$ miles. Use $d=st$: $12 imes 2.5=30$ miles.
$30$ miles. Use $d=st$: $12 imes 2.5=30$ miles.
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Solve a work-rate problem: One machine makes $30$ parts per hour. How many parts in $20$ minutes?
Solve a work-rate problem: One machine makes $30$ parts per hour. How many parts in $20$ minutes?
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$10$ parts. $20$ min $= rac{1}{3}$ hr, so $30 imes rac{1}{3}=10$.
$10$ parts. $20$ min $= rac{1}{3}$ hr, so $30 imes rac{1}{3}=10$.
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Compute a percent increase: A price rises from $50$ to $60$. What is the percent increase?
Compute a percent increase: A price rises from $50$ to $60$. What is the percent increase?
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$20%$. Use $ rac{60-50}{50} imes 100%= rac{10}{50} imes 100%$.
$20%$. Use $ rac{60-50}{50} imes 100%= rac{10}{50} imes 100%$.
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Find the constant of proportionality: If $y=18$ when $x=6$ in a proportional relationship, what is $k$?
Find the constant of proportionality: If $y=18$ when $x=6$ in a proportional relationship, what is $k$?
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$3$. Find $k$ using $k= rac{y}{x}= rac{18}{6}=3$.
$3$. Find $k$ using $k= rac{y}{x}= rac{18}{6}=3$.
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