Question

course 2 chapter 1 study guide proportional relationships

1. the table shows how fast some of the worlds fastest animals could travel in different portions of an hour at their top speed. write the names of the animals in order from least to greatest speed in miles per hour.

animal	distance (mi)	time (h)
brown hare	8	1/6
cheetah	7	1/10
elk	18	2/5

1. city carpet advertises that they can install 1,200 square feet of carpet in 2 1/2 hours. place an x in the correct cell to indicate whether each rate below is equivalent to this rate.

	equivalent	not equivalent
b 1,000 square feet of carpet in 1 3/4 hours
c 1,560 square feet of carpet in 3 1/4 hours

Explanation:

Step1: Calculate speed of each animal

Speed = $\frac{\text{Distance}}{\text{Time}}$. For Blue Wildebeest: $\frac{33\frac{1}{3}}{\frac{2}{3}}=\frac{\frac{100}{3}}{\frac{2}{3}}=\frac{100}{3}\times\frac{3}{2} = 50$ miles per hour. For Brown Hare: $\frac{8}{\frac{1}{6}}=8\times6 = 48$ miles per hour. For Cheetah: $\frac{7}{\frac{1}{10}}=7\times10 = 70$ miles per hour. For Elk: $\frac{18}{\frac{2}{5}}=18\times\frac{5}{2}=45$ miles per hour.

Step2: Order the speeds

The order from least - to greatest speed is Elk (45 mph), Brown Hare (48 mph), Blue Wildebeest (50 mph), Cheetah (70 mph).

Step3: Calculate the rate of City Carpet

City Carpet rate: $\frac{1200}{2\frac{1}{2}}=\frac{1200}{\frac{5}{2}}=1200\times\frac{2}{5}=480$ square feet per hour.

Step4: Check each option for City Carpet

Option A: $\frac{960}{2}=480$ square feet per hour (equivalent). Option B: $\frac{1000}{1\frac{3}{4}}=\frac{1000}{\frac{7}{4}}=1000\times\frac{4}{7}=\frac{4000}{7}\approx571.43$ square feet per hour (not equivalent). Option C: $\frac{1560}{3\frac{1}{4}}=\frac{1560}{\frac{13}{4}}=1560\times\frac{4}{13}=480$ square feet per hour (equivalent).

Answer:

1. Elk, Brown Hare, Blue Wildebeest, Cheetah
2. A. equivalent

B. not equivalent
C. equivalent