Rates and Unit Rates: Additional Practice (Set 1)

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

$\frac{7 \text{ gallons}}{4 \text{ seconds}} = \frac{7 \times 15}{4 \times 15} = \frac{105 \text{ gallons}}{60 \text{ seconds}}$

The pool fills $105$ gallons in one minute.

Each hour covers $72$ miles, so the time is how many groups of $72$ miles fit in $252$ miles, a division.

$252 \div 72 = 3.5$

It takes $3.5$ hours.

Find the price per pound for each roast.

$\text{A: } 30 \div 4 = 7.50 \qquad \text{B: } 21 \div 3 = 7.00$

Roast B is $7.00$ per pound against A's $7.50$, so B is cheaper. Subtract to find by how much.

$7.50 - 7.00 = 0.50$

So Roast B is cheaper by $0.50$ per pound.

Speed in miles per hour is miles for a single hour, so divide the miles by the hours.

$1{,}260 \div 2.25 = 560$

The jet's speed is $560$ miles per hour.

One hour is $60$ minutes, and each minute drips $0.2$ liters, so multiply.

$0.2 \times 60 = 12$

The faucet drips $12$ liters in one hour.

Find the second car's miles per gallon.

$480 \div 12 = 40$

The second car gets $40$ miles per gallon against the first's $30$, so the second is more efficient. Subtract to find by how much.

$40 - 30 = 10$

The second car is more efficient by $10$ miles per gallon.

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

$20 \div 2.5 = 8.00$

The coffee costs $8.00$ dollars per pound.

First find the speed in miles per hour.

$135 \div 1.5 = 90 \text{ miles per hour}$

Then scale up to $6$ hours by multiplying.

$90 \times 6 = 540$

The train travels $540$ miles.

Find the bag's price per ounce.

$6.00 \div 12 = 0.50 \text{ dollars per ounce}$

The bag is $0.50$ per ounce against $0.60$ loose. Subtract to find the saving per ounce.

$0.60 - 0.50 = 0.10$

So you save $0.10$ per ounce.

Two minutes is $120$ seconds, which is $15$ times $8$ seconds, so scale both quantities by $15$.

$\frac{3 \text{ parts}}{8 \text{ seconds}} = \frac{3 \times 15}{8 \times 15} = \frac{45 \text{ parts}}{120 \text{ seconds}}$

The robot assembles $45$ parts.

Write the time in hours: $3$ hours and $30$ minutes is $3.5$ hours. Multiply the speed by the time.

$50 \times 3.5 = 175$

The car travels $175$ miles.

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

$\text{P: } 5 \div 400 = 0.0125 \qquad \text{Q: } 3 \div 250 = 0.012$

Brand Q is lower at $0.012$ dollars per gram.