Lesson 9
Constant Speed
Problem 1
Han ran 10 meters in 2.7 seconds. Priya ran 10 meters in 2.4 seconds.
- Who ran faster? Explain how you know.
- At this rate, how long would it take each person to run 50 meters? Explain or show your reasoning.
Solution
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Problem 2
A scooter travels 30 feet in 2 seconds at a constant speed.
![Double number line. Distance, feet. Time, seconds.](https://cms-im.s3.amazonaws.com/zaoMAu7son8Eb5yGxr9rz6Yr?response-content-disposition=inline%3B%20filename%3D%226-6.2.C4.PP.Image.Rev.0101.png%22%3B%20filename%2A%3DUTF-8%27%276-6.2.C4.PP.Image.Rev.0101.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240630%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240630T171853Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=d4e6b1ed887e0f9ba806cdf956b42aa5e4c1120a69fc34acf2bb34fbe2087077)
- What is the speed of the scooter in feet per second?
- Complete the double number line to show the distance the scooter travels after 1, 3, 4, and 5 seconds.
- A skateboard travels 55 feet in 4 seconds. Is the skateboard going faster, slower, or the same speed as the scooter?
Solution
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Problem 3
A cargo ship traveled 150 nautical miles in 6 hours at a constant speed. How far did the cargo ship travel in one hour?
![Double number line. Distance traveled, nautical miles. Elapsed time, hours.](https://cms-im.s3.amazonaws.com/gt7D36Jwnr5BW3CNtTjCCk5X?response-content-disposition=inline%3B%20filename%3D%226-6.2.C.PP_Image_15.png%22%3B%20filename%2A%3DUTF-8%27%276-6.2.C.PP_Image_15.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240630%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240630T171853Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=3ac82395cdd7aabc956bc7dfbd4097e26750e353d887c4773dc80f048037bfb9)
Solution
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Problem 4
A recipe for pasta dough says, “Use 150 grams of flour per large egg.”
- How much flour is needed if 6 large eggs are used?
-
How many eggs are needed if 450 grams of flour are used?
Solution
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(From Unit 2, Lesson 3.)Problem 5
The grocery store is having a sale on frozen vegetables. 4 bags are being sold for $11.96. At this rate, what is the cost of:
- 1 bag
- 9 bags
Solution
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(From Unit 2, Lesson 8.)Problem 6
A pet owner has 5 cats. Each cat has 2 ears and 4 paws.
- Complete the double number line to show the numbers of ears and paws for 1, 2, 3, 4, and 5 cats.
- If there are 3 cats in the room, what is the ratio of ears to paws?
![Double number line. 1 tick mark. Top line, number of ears. Tick mark labled 0. Bottom line, number of paws. Tick mark labled 0.](https://cms-im.s3.amazonaws.com/UmgJ7TaJL1q63svK1yyCvtDd?response-content-disposition=inline%3B%20filename%3D%226-6.2.C2.PP.Image.Rev.0101.png%22%3B%20filename%2A%3DUTF-8%27%276-6.2.C2.PP.Image.Rev.0101.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240630%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240630T171853Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=f9e37276f61ca5ea80e118f3ce4ac92dbfdfa8de081aaa15c3ee0a88f886dda8)
- If there are 4 cats in the room, what is the ratio of paws to ears?
- If all 5 cats are in the room, how many more paws are there than ears?
Solution
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(From Unit 2, Lesson 7.)Problem 7
Each of these is a pair of equivalent ratios. For each pair, explain why they are equivalent ratios or draw a representation that shows why they are equivalent ratios.
- \(5:1\) and \(15:3\)
- \(25:5\) and \(10:2\)
- \(198:1,\!287\) and \(2:13\)
Solution
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(From Unit 2, Lesson 5.)