Rates and Unit Rates: Practice

The unit rate is $80$ miles per hour, so each hour covers $80$ miles. The number of hours is how many groups of $80$ miles fit in $360$ miles, which is a division.

$360 \div 80 = 4.5$

It takes $4.5$ hours.

One minute is $60$ seconds, which is $15$ times $4$ seconds, so scale both quantities by $15$.

$\frac{5 \text{ pages}}{4 \text{ seconds}} = \frac{5 \times 15}{4 \times 15} = \frac{75 \text{ pages}}{60 \text{ seconds}}$

The printer prints $75$ pages in $1$ minute.

The unit rate is $2 \div 3$ cups per serving, but it is cleaner to scale: $12$ servings is $4$ times $3$ servings, so scale both quantities by $4$.

$\frac{2 \text{ cups}}{3 \text{ servings}} = \frac{2 \times 4}{3 \times 4} = \frac{8 \text{ cups}}{12 \text{ servings}}$

You need $8$ cups of broth.

Find each pump's unit rate in gallons per minute.

$\text{A: } 40 \div 5 = 8 \qquad \text{B: } 54 \div 6 = 9$

Pump B moves $9$ gallons per minute against A's $8$, so B is faster. Subtract to find by how much.

$9 - 8 = 1$

So Pump B is faster by $1$ gallon per minute.

Find each car's miles per gallon by dividing miles by gallons.

$\text{first: } 210 \div 7 = 30 \qquad \text{second: } 192 \div 6 = 32$

The second car gets $32$ miles per gallon, more than the first at $30$, so the second car is more fuel-efficient.

Multiply the price per pound by the number of pounds.

$2.40 \times 3.5 = 8.40$

The apples cost $8.40$ dollars.

First find the unit rate in copies per minute.

$480 \div 8 = 60 \text{ copies per minute}$

Then scale up to $20$ minutes by multiplying.

$60 \times 20 = 1{,}200$

The copier makes $1{,}200$ copies.

Find the price per vitamin for each bottle.

$\text{small: } 5 \div 20 = 0.25 \qquad \text{large: } 11 \div 50 = 0.22$

Subtract the two unit prices to find the saving per vitamin.

$0.25 - 0.22 = 0.03$

The larger bottle saves $0.03$ per vitamin.

Find each leg's distance by multiplying its speed by its time.

$55 \times 2 = 110 \qquad 65 \times 3 = 195$

Add the two legs to get the total distance.

$110 + 195 = 305$

The total distance is $305$ miles.

Price per pound is dollars for a single pound, so divide the dollars by the pounds.

$9 \div 2.5 = 3.60$

The cheese costs $3.60$ dollars per pound.

First find the speed in miles per hour.

$90 \div 1.5 = 60 \text{ miles per hour}$

Then scale up to $4$ hours by multiplying.

$60 \times 4 = 240$

The train goes $240$ miles.

The rate is $8$ minutes per $5$ laps. Since $20$ laps is $4$ times $5$ laps, scale both quantities by $4$.

$\frac{8 \text{ minutes}}{5 \text{ laps}} = \frac{8 \times 4}{5 \times 4} = \frac{32 \text{ minutes}}{20 \text{ laps}}$

So $20$ laps takes $32$ minutes.