Question

(after) winter break review packet - due monday 1/13/20
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 $1\frac{1}{4}$ pounds of ham for $14.50.
• someone bought $2\frac{1}{2}$ pounds of turkey for $26.25.
• someone bought $\frac{3}{4}$ pound of roast beef for $8.50.

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: Find speed (miles/hour)

Step1: Convert mixed numbers to fractions
$3\frac{1}{4} = \frac{13}{4}$, $\frac{1}{10}$ remains as is.
Step2: Divide distance by time
$\text{Speed} = \frac{\frac{13}{4}}{\frac{1}{10}} = \frac{13}{4} \times 10 = \frac{130}{4} = \frac{65}{2} = 32.5$

Problem 1b: Find time for $4\frac{1}{2}$ miles

Step1: Convert distance to fraction
$4\frac{1}{2} = \frac{9}{2}$
Step2: Divide distance by speed
$\text{Time} = \frac{\frac{9}{2}}{\frac{65}{2}} = \frac{9}{2} \times \frac{2}{65} = \frac{9}{65}$ hours

Problem 2: Find unit prices of meats

Step1: Calculate ham's unit price
$1\frac{1}{2} = \frac{3}{2}$, $\text{Ham price} = \frac{14.50}{\frac{3}{2}} = 14.50 \times \frac{2}{3} \approx 9.67$ dollars/pound
Step2: Calculate turkey's unit price
$2\frac{1}{2} = \frac{5}{2}$, $\text{Turkey price} = \frac{28.25}{\frac{5}{2}} = 28.25 \times \frac{2}{5} = 11.30$ dollars/pound
Step3: Calculate roast beef's unit price
$\text{Roast beef price} = \frac{5.50}{\frac{2}{3}} = 5.50 \times \frac{3}{2} = 8.25$ dollars/pound
Step4: Compare unit prices
$8.25 < 9.67 < 11.30$

Problem 3: Find time for 3 apples

Step1: Find rate of apple consumption
$\text{Rate} = \frac{\frac{1}{2}\text{ apple}}{3\text{ days}} = \frac{1}{6}$ apples/day
Step2: Divide total apples by rate
$\text{Time} = \frac{3}{\frac{1}{6}} = 3 \times 6 = 18$ days

Answer:

1a. $32.5$ miles per hour
1b. $\frac{9}{65}$ hours

1. The least expensive per pound is roast beef ($\$8.25$), and the most expensive per pound is turkey ($\$11.30$). This is determined by calculating the unit price (total cost divided by weight) for each meat and comparing the values.
2. 18 days