Rates
Unit Rates
Real World Problems
Vocabulary
Review
100
A car traveled a distance of 192 miles form New York to a small town in Pennsylvania in 3 hours. Find the speed of the car.
The speed of the car is 64 miles per hour.
100
It took Daniel 3 hours to paint his bedroom, which was 285 square feet of surface area. How many square feet can Daniel paint in 1 hour?
Daniel can paint 95 square feet per hour.
100
A train moved at a speed of 90 miles per hour for 2 hours and then slowed down to 72 miles per hour for the next 30 minutes. What is the total number of miles traveled in 2.5 hours? What was the average speed of the train?
The train traveled 216 miles in 2 and a half hours. The average speed of the train is 86.4 miles per hour.
100
What is a rate?
A ratio that compares two quantities with DIFFERENT units.
100
What does the word "of" mean in math?
The word "of" means to multiply in a math context.
200
A wheel can make 80 revolutions every two minutes. At this rate, how many minutes does it take the wheel to make 280 revolutions?
It takes 7 minutes for the wheel to make 280 revolutions.
200
Dr. Cohen drives his car 96 miles in 1.5 hours. What is the unit rate? If Dr. Cohen continues to drive at this rate how many miles will he travel in 2.5 hours?
Dr. Cohen's unit rate of speed is 64 miles per hour. If he continues to drive at this rate he will travel 160 miles in 2.5 hours.
200
Ms. Survis takes 4 hours to drive 210 miles from her home to Yosemite National Park. If Ms. Survis' average speed is 60 miles per hour for the first two hours, find her average speed for the last two hours.
Ms. Survis average speed for the last two hours is 45 miles per hour.
200
What is a unit rate?
A ratio that compares a quantity to ONE UNIT of a different quantity.
200
When dividing fractions what do you do to the 2nd fraction? What is the mathematical term for this action?
When dividing fractions you flip the 2nd fraction, this is called the reciprocal.
300
The flow rate of a water pump is 2.8 gallons per minute. How many minutes does it take this pump to transfer 84 gallons of water out of a swimming pool?
It takes the pump 30 minutes to transfer 84 gallons of water.
300
Anna swims 490 meters in 5 minutes. Find the unit rate, her swimming speed per minute. How far will Anna swim in 10 minutes at this rate?
Anna's unit rate of speed is 98 meters per minute. At this rate she will swim 980 meters in 10 minutes.
300
Tyler walks home from school at a speed of 5 kilometers per hour. He takes 12 minutes to reach home. What is the distance between the school and his home? (Hint: convert the time from minutes to hours).
The distance between the school and his home is 1 kilometer.
300
How is speed calculated?
Speed is calculated by dividing the distance by the amount of time it took to go that distance.
300
What does the term simplest form refer to?
Simplest form means that you reduce the answer to the smallest number it can be, or the unit to the most simplified unit it can be.
400
Evan makes $17.50 per lawn mowing lawns. How much will he make for mowing 2 lawns? 3 lawns? 4 lawns? 5 lawns? 20 lawns? How many lawns will Evan have to mow to make $500?
Evan will make $35 for two lawns, $52.50 for three lawns, $70 for four lawns, $87.50 for five lawns, and $350 for 20 lawns. Evan would have to mow 29 lawns to make $500 because he would only make $490 if he mows 28 lawns. He would need to mow one additional lawn to reach the $500 mark.
400
A sprinkler system is designed to water 5/8 of an acre in 1/4 of an hour. How many acres of land can it water in 1 hour? How many acres of land can be watered in 5 hours?
The sprinkler system can water 2.5 acres of land in 1 hour. In 5 hours 12.5 acres of land can be watered.
400
Mei took a total of 9 quizzes over the course of 3 weeks. After attending 5 weeks of school this quarter, how many quizzes will Mei have taken in total? What is the unit rate for this problem?
Mei took 15 quizzes in 5 weeks. The unit rate for this problem is 3 quizzes per week.
400
How is average speed calculated?
Average speed is calculated by dividing the total distance traveled by the total time it took to go that distance.
400
Solve. a. 12 divided by 9/10 = b. 5/8 divided by 15/16=
What is
a. 13 1/3
b. 2/3
500
The table shows the cost of three different vegetables.
Fill in the missing pieces of the table. Which type of vegetable costs the most per pound? What is the price difference per pound between each of three vegetables?
The missing pieces of the table are as follows:
Cost of okra: $3.75 / pound
Tomatoes Purchased: 5.5 pounds
Total cost of Zucchini: $15.70
The vegetable that costs the most per pound is tomatoes. The least expensive vegetable is zucchini. The price difference between zucchini and okra is $0.76 per pound. The price difference between okra and tomatoes is $1.24 per pound.
500
India can solve 100 multiplication problems in 2 minutes and 45 seconds. How many problems can India solve in 1 minute? How many can she solve in 30 seconds? In 5 minutes?
India can solve 36.4 problems per minute. In 30 seconds India can solve 18.2 problems and in 5 minutes India can solve 182 multiplication problems.
500
A truck traveled from Town A to Town B, and then to Town C. The truck took 3 hours to travel from Town A to Town B at an average speed of 42 kilometers per hour. It then traveled from Town B to Town C at an average speed of 68 kilometers per hour. The truck took a total of 5 hours to travel from Town A to Town C.
A. What is the distance between Town A and Town B?
B. What was the average speed of the truck for the whole journey?
A. The distance between Town A and Town B is 126 kilometers.
B. The average speed for the whole journey was 52.4 kilometers per hour.
500
How is distance calculated?
Distance is calculated by multiplying speed by the amount of time it took to travel.
500
Solve. 12 2/3 divided by 5 11/13.
What is 2 1/6.