Lesson 9
Constant Speed
Let’s use ratios to work with how fast things move.
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.
Problem 2
A scooter travels 30 feet in 2 seconds at a constant speed.
![Double number line. Distance, feet. Time, seconds.](https://staging-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=AKIAXQCCIHWF37H2AMFB%2F20240703%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240703T093725Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=cb13bdbc3e1670439cd431a01fe2e645f34203af641c03a7b85a7c249e05bdaa)
- 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?
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://staging-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=AKIAXQCCIHWF37H2AMFB%2F20240703%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240703T093725Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=b55816a7879a4e4a96d08d9bf984e2e771e0bd972479e13122933e68eca71483)
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?
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
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://staging-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=AKIAXQCCIHWF37H2AMFB%2F20240703%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240703T093725Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=3dc41cac402d0acb35dcb6f9e4e510a72795e337551e1e781cd4073bd4582886)
- 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?
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 \(2:13\)