Question

1. a person jogs 13 mile in 2.6 hours. what is the persons speed in miles per hour? dont forget your labels!

1. you are helping to make crusader soup. you mixed ingredient a: $2\\ \frac{1}{2}$ gallon with every $3\\ \frac{1}{4}$ gallons of ingredient b. how many gallons of each ingredient will you need to make 92 gallons of crusader soup?

hint: a + b = total gallons.
$2.5 + 3.25 = 5.75$ \\(\frac{2.5}{5.75}=\frac{?}{92}\\) \\(\frac{3.25}{5.75}=\frac{?}{92}\\)

1. you kayak up a river at a rate of 48 feet every 30 seconds. you kayak 423 feet every 3 minutes on the way back down the river. how much further do you kayak in 5 minutes on the way down the river than in 5 minutes on the way up the river?

1. complete the table

\

$$\begin{tabular}{|l|l|l|l|} \\hline miles & 24 & 8 & \\\\ \\hline hours & $\\frac{3}{4}$ & & $\\frac{1}{2}$\\\\ \\hline \\end{tabular}$$

Explanation:

Question 11

Step1: Recall speed formula

$\text{Speed} = \frac{\text{Distance}}{\text{Time}}$

Step2: Substitute given values

$\text{Speed} = \frac{13}{2.6}$

Step3: Calculate the result

$\text{Speed} = 5$ miles per hour

Question 12

Step1: Find ratio for Ingredient A

Let $A$ = gallons of A. $A = 92 \times \frac{2.5}{5.75}$

Step2: Calculate Ingredient A

$A = 92 \times \frac{10}{23} = 40$ gallons

Step3: Find ratio for Ingredient B

Let $B$ = gallons of B. $B = 92 \times \frac{3.25}{5.75}$

Step4: Calculate Ingredient B

$B = 92 \times \frac{13}{23} = 52$ gallons

Question 13

Step1: Convert upriver rate to ft/min

Upriver rate: $\frac{48 \text{ ft}}{0.5 \text{ min}} = 96$ ft/min

Step2: Calculate upriver distance in 5 min

Upriver distance: $96 \times 5 = 480$ ft

Step3: Convert downriver rate to ft/min

Downriver rate: $\frac{423 \text{ ft}}{3 \text{ min}} = 141$ ft/min

Step4: Calculate downriver distance in 5 min

Downriver distance: $141 \times 5 = 705$ ft

Step5: Find distance difference

Difference: $705 - 480 = 225$ ft

Question 14

Step1: Find constant speed

Speed = $\frac{24}{\frac{3}{4}} = 24 \times \frac{4}{3} = 32$ mph

Step2: Calculate time for 8 miles

Time = $\frac{8}{32} = \frac{1}{4}$ hours

Step3: Calculate miles for $\frac{1}{2}$ hour

Miles = $32 \times \frac{1}{2} = 16$ miles

Answer:

1. 5 miles per hour
2. Ingredient A: 40 gallons, Ingredient B: 52 gallons
3. 225 feet
4. Hours for 8 miles: $\frac{1}{4}$; Miles for $\frac{1}{2}$ hour: 16