Question

independent practice

1. andrew has a part - time job at a bakery. he works 3 hours a day, monday through friday. it takes andrew an average of 17 minutes to decorate a cake. estimate how many cakes andrew can decorate in a week.

a. 5
b. 60
c. 300
d. 15,000

1. danny pedals his bike at a rate of 75 tire revolutions per minute. for each revolution, his bike travels 1.4 meters. at this rate, how long will it take for danny to travel 5 kilometers?

a. 1.9 min
b. 47.6 min
c. 93.3 min
d. 525,000 min

1. a stone is a unit of weight equal to 14 pounds. a panda gains 1 stone in 6 weeks. at this rate, how many days would it take the panda to gain 15 pounds?

a. 3 days
b. 6 days
c. 45 days
d. 48 days

1. a robot travels at a speed of 3 miles per hour. what is the robots approximate speed in feet per second?

a. 1.47 feet per second
b. 4.4 feet per second
c. 13.2 feet per second
d. 26.4 feet per second
read the information below. then answer questions 7 and 8.
lilly fills a 10 - gallon cooler with sports drink for her soccer team. each player drinks 16 ounces per hour.

1. how many gallons per minute does each player drink?

a. \\( \frac{1}{480} \\) gal per min
b. \\( \frac{1}{120} \\) gal per min
c. \\( \frac{1}{60} \\) gal per min
d. 120 gal per min

1. how long would it take 10 players to drink all of the sports drink in the cooler?

a. \\( \frac{1}{48} \\) min
b. 48 min
c. 480 min
d. 4,800 min

1. a rocket travels 204 meters per second. the rocket begins a navigational correction after it has traveled 55 kilometers. after about how many minutes does the navigational correction begin?

a. 0.2 min
b. 4.5 min
c. 45.5 min
d. 270.0 min

1. a car is traveling at a speed of 75 feet per second. what is the cars speed in miles per hour?

a. 23.47 mph
b. 51.14 mph
c. 70.4 mph
d. 153.4 mph

Explanation:

Step1: Convert units for problem 7

We know that \(1\) gallon \( = 128\) ounces and \(1\) hour \(=60\) minutes. Each player drinks \(16\) ounces per hour. First, convert the amount of drink per hour to gallons per hour: \(\frac{16}{128}=\frac{1}{8}\) gallons per hour. Then convert gallons per hour to gallons per minute. Using the formula \(v=\frac{\text{gallons}}{\text{hour}}\times\frac{\text{hour}}{\text{minute}}\), we have \(\frac{1}{8}\times\frac{1}{60}=\frac{1}{480}\) gallons per minute.

Step2: Solve problem 8

The cooler has \(10\) gallons. Each player drinks \(\frac{1}{480}\) gallons per minute. For \(10\) players, the rate is \(10\times\frac{1}{480}=\frac{1}{48}\) gallons per minute. Using the formula \(t = \frac{\text{volume}}{\text{rate}}\), with volume \(V = 10\) gallons and rate \(r=\frac{1}{48}\) gallons per minute, \(t=\frac{10}{\frac{1}{48}}=480\) minutes.

Step3: Solve problem 9

The rocket speed \(v = 204\) meters per second. The distance \(d=55\) kilometers \(=55\times1000 = 55000\) meters. First, find the time in seconds using \(t=\frac{d}{v}=\frac{55000}{204}\approx269.61\) seconds. Then convert seconds to minutes: \(t=\frac{269.61}{60}\approx4.5\) minutes.

Step4: Solve problem 10

We know that \(1\) mile \( = 5280\) feet and \(1\) hour \(=3600\) seconds. The car speed is \(75\) feet per second. Using the formula \(v=\frac{\text{feet}}{\text{second}}\times\frac{\text{second}}{\text{hour}}\times\frac{\text{mile}}{\text{feet}}\), we have \(v = 75\times\frac{3600}{1}\times\frac{1}{5280}\approx51.14\) miles per hour.

Step5: Solve problem 3

Andrew works \(3\) hours a day, \(5\) days a week, so \(3\times5 = 15\) hours a week. Each cake takes \(17\) minutes (\(\frac{17}{60}\) hours). The number of cakes \(n=\frac{15}{\frac{17}{60}}\approx52.94\approx50\) (after estimation).

Step6: Solve problem 4

Danny's speed: Each revolution is \(1.4\) meters, \(75\) revolutions per minute. So speed \(v=1.4\times75 = 105\) meters per minute. \(5\) kilometers \(=5000\) meters. Time \(t=\frac{5000}{105}\approx47.6\) minutes.

Step7: Solve problem 5

A stone is \(14\) pounds. The panda gains \(14\) pounds in \(6\) weeks (\(6\times7 = 42\) days). The rate of weight gain is \(\frac{14}{42}=\frac{1}{3}\) pounds per day. To gain \(15\) pounds, \(t=\frac{15}{\frac{1}{3}} = 45\) days.

Step8: Solve problem 6

The robot speed is \(3\) miles per hour. \(1\) mile \(=5280\) feet, \(1\) hour \(=3600\) seconds. Using the formula \(v=\frac{\text{miles}}{\text{hour}}\times\frac{\text{feet}}{\text{mile}}\times\frac{\text{hour}}{\text{second}}\), \(v=3\times\frac{5280}{3600}=4.4\) feet per second.

Answer:

1. A. 5
2. B. 47.6 min
3. C. 45 days
4. B. 4.4 feet per second
5. A. \(\frac{1}{480}\) gal per min
6. C. 480 min
7. B. 4.5 min
8. B. 51.14 mph