Rate Work Problems

Video Solutions to help Grade 6 students learn how to solve constant rate work problems by calculating and comparing unit rates.

Lesson 23 Outcome

• Students solve constant rate work problems by calculating and comparing unit rates.

Lesson 23 Summary

• Constant rate problems always count or measure something happening per unit of time. The time is always in the denominator.
• Sometimes the units of time in the denominators of two rates are not the same. One must be converted to the other before calculating the unit rate of each.
• Dividing the numerator by the denominator calculates the unit rate; this number stays in the numerator. The number in the denominator of the equivalent fraction is always 1.

NYS Math Module 1 Grade 6 Lesson 23 Classwork

Example 1: Fresh-Cut Grass
Suppose that on a Saturday morning you can cut 3 lawns in 5 hours, and your friend can cut 5 lawns in 8 hours. Your friend claims he is working faster than you. Who is cutting lawns at a faster rate? How do you find out?

Example 2: Restaurant Advertising
Next, suppose you own a restaurant. You want to do some advertising, so you hire 2 middle school students to deliver take-out menus around town. One of them, Darla, delivers 350 menus in 2 hours, and another employee, Drew, delivers 510 menus in 3 hours. You promise a \$10 bonus to the fastest worker since time is money in the restaurant business. Who gets the bonus?

Example 3: Survival of the Fittest
Which runs faster: a cheetah that can run 60 feet in 4 seconds or gazelle that can run 100 feet in 8 seconds?

Example 4: Flying Fingers
What if the units of time are not the same in the two rates? The secretary in the main office can type 225 words in 3 minutes, while the computer teacher can type 105 words in 90 seconds. Who types at a faster rate?

Problem Set
1. Who walks at a faster rate: someone who walks 60 feet in 10 seconds or someone who walks 42 feet in 6 seconds?

2. Who walks at a faster rate: someone who walks 60 feet in 10 seconds or someone who takes 5 seconds to walk 25 feet? Review the lesson summary before answering!

3. Which parachute has a slower decent: a red parachute that falls 10 feet in 4 seconds or a blue parachute that falls 12 feet in 6 seconds?

4. During the winter of 2012-2013, Buffalo, New York received 22 inches of snow in 12 hours. Oswego, New York received 31 inches of snow over a 15 hour period. Which city had a heavier snowfall rate? Round your answers to the nearest hundredth.

5. A striped marlin can swim at a rate of 70 miles per hour. Is this a faster or slower rate than a sailfish, which takes 30 minutes to swim 40 miles?

6. One math student, John, can solve these 6 math problems in 20 minutes while another student, Juaquine, can solve them at a rate of 1 problem per 4 minutes. Who works faster?

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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