Rates and Unit Rates: Additional Practice (Set 2)

First find the unit rate in miles per gallon by dividing miles by gallons.

$384 \div 12 = 32 \text{ miles per gallon}$

Then scale up to $5$ gallons by multiplying.

$32 \times 5 = 160$

The car can travel $160$ miles on $5$ gallons.

First find the speed in miles per hour.

$266 \div 7 = 38 \text{ miles per hour}$

Then scale up to $4$ hours by multiplying.

$38 \times 4 = 152$

The van travels $152$ miles.

Find the price per ounce for each size by dividing dollars by ounces.

$\text{A: } 3.00 \div 15 = 0.20 \qquad \text{B: } 4.80 \div 24 = 0.20$

Both come to $0.20$ dollars per ounce, so they cost the same per ounce.

Price per yogurt is dollars for a single yogurt, so divide the dollars by the count.

$4.20 \div 6 = 0.70$

Each yogurt costs $0.70$ dollars.

A day is $24 \times 60 = 1{,}440$ minutes. The leak is $40$ minutes per $3$ liters, so the number of $40$-minute blocks in a day is $1{,}440 \div 40 = 36$, and each block leaks $3$ liters.

$36 \times 3 = 108$

So $108$ liters leak in a day.

First find the unit rate in pages per cartridge.

$1{,}200 \div 3 = 400 \text{ pages per cartridge}$

Then scale up to $5$ cartridges by multiplying.

$400 \times 5 = 2{,}000$

It can print $2{,}000$ pages.

The unit rate is $9 \div 2 = 4.5$ jars per minute. The time to fill $63$ jars is how many minutes are needed at that rate, found by dividing jars by the per-minute rate.

$63 \div 4.5 = 14$

It takes $14$ minutes.

Since $14$ days is $7$ times $2$ days, scale both quantities by $7$.

$\frac{5 \text{ fences}}{2 \text{ days}} = \frac{5 \times 7}{2 \times 7} = \frac{35 \text{ fences}}{14 \text{ days}}$

The team can paint $35$ fences.

Each minute removes $0.5$ liters, so the number of minutes is how many half-liters are in $18$ liters, found by dividing.

$18 \div 0.5 = 36$

It takes $36$ minutes to empty.

Multiply the price per gallon by the number of gallons.

$3.60 \times 12.5 = 45.00$

The gas costs $45.00$ dollars.

Find the price per gram for each brand by dividing dollars by grams.

$\text{X: } 6 \div 750 = 0.008 \qquad \text{Y: } 4.50 \div 500 = 0.009$

Brand X is cheaper at $0.008$ dollars per gram, so it is the better value.

Since $45$ minutes is $9$ times $5$ minutes, scale both quantities by $9$.

$\frac{11 \text{ boxes}}{5 \text{ minutes}} = \frac{11 \times 9}{5 \times 9} = \frac{99 \text{ boxes}}{45 \text{ minutes}}$

The machine packs $99$ boxes.