Question

(after) winter break review packet - due monday 1/12/26
1.
a cyclist rode $3\frac{3}{4}$ miles in $\frac{3}{10}$ hour.
a. how fast was she going in miles per hour?

b. at that rate, how long will it take her to go $4\frac{1}{2}$ miles?

2.
at a deli counter,

• someone bought $1\frac{3}{4}$ pounds of ham for $14.50.
• someone bought $2\frac{1}{2}$ pounds of turkey for $26.25.
• someone bought $\frac{3}{8}$ pound of roast beef for $5.50.

which meat is the least expensive per pound? which meat is the most expensive per pound? explain how you know.

3.
it takes an ant farm 3 days to consume $\frac{1}{2}$ of an apple. at that rate, in how many days will the ant farm consume 3 apples?

Explanation:

Problem 1a

Step1: Convert mixed number to improper fraction

$3\frac{3}{4} = \frac{15}{4}$

Step2: Calculate speed (distance ÷ time)

$\text{Speed} = \frac{15}{4} \div \frac{3}{10} = \frac{15}{4} \times \frac{10}{3} = \frac{150}{12} = \frac{25}{2} = 12.5$

Problem 1b

Step1: Convert distance to improper fraction

$4\frac{1}{2} = \frac{9}{2}$

Step2: Time = distance ÷ speed

$\text{Time} = \frac{9}{2} \div \frac{25}{2} = \frac{9}{2} \times \frac{2}{25} = \frac{9}{25} = 0.36$ hours

Problem 2

Step1: Calculate ham price per pound

$1\frac{3}{4} = \frac{7}{4}$, $\text{Ham rate} = 14.50 \div \frac{7}{4} = 14.50 \times \frac{4}{7} \approx 8.29$ dollars/pound

Step2: Calculate turkey price per pound

$2\frac{1}{2} = \frac{5}{2}$, $\text{Turkey rate} = 26.25 \div \frac{5}{2} = 26.25 \times \frac{2}{5} = 10.50$ dollars/pound

Step3: Calculate roast beef price per pound

$\text{Roast beef rate} = 5.50 \div \frac{3}{8} = 5.50 \times \frac{8}{3} \approx 14.67$ dollars/pound

Step4: Compare the three rates

$8.29 < 10.50 < 14.67$

Problem 3

Step1: Find rate of apple consumption

$\text{Rate} = \frac{1}{2} \text{ apple} \div 3 \text{ days} = \frac{1}{6}$ apples/day

Step2: Calculate time for 3 apples

$\text{Time} = 3 \div \frac{1}{6} = 3 \times 6 = 18$ days

Answer:

1a. $12.5$ miles per hour
1b. $\frac{9}{25}$ (or 0.36) hours

1. The least expensive per pound is ham ($\approx\$8.29$), and the most expensive per pound is roast beef ($\approx\$14.67$). This is determined by calculating the price per pound for each meat and comparing the values.
2. 18 days