Algebra 2 Pre-Unit
Name: _________________________________
Investigation 3 WS
Hour: ________
Date: ______________
1. What does it mean for an object to move at a constant speed? (Note: Please say something more than “the
speed doesn’t change” – be descriptive and reference specific quantities.)
2. Jenny was riding her bike along a path. Assume that she rode at a constant speed during the entire ride, and
also suppose that during one part of the trip she rode 88 feet in 6 seconds.
a. Provide at least four conclusions we can draw from the given information.
b. During this interval, how far did Jenny travel in 5 seconds?
c. Does your answer to part (b) depend on which 5-second interval we’re talking about? Explain.
d. How long did it take Jenny to travel any 10-foot distance during this part of her ride?
3. Paul was walking in a park. Assume that he walked at a constant speed during the entire trip, and also suppose
that during one part of the trip he walked 52.8 feet in 8 seconds.
a. Provide at least four conclusions we can draw from the given information.
b. During this interval, how far did Paul travel in 14 seconds?
c. Does your answer to part (b) depend on which 14-second interval we’re talking about? Explain.
d. How long did it take Paul to travel any 20-foot distance during this part of his ride?
4. Assume that a football and a soccer ball are both traveling at constant speeds (but not necessarily the same
constant speed as each other).
a. What does it mean to say that the soccer ball is traveling faster than the football? Be descriptive, and
reference the specific quantities involved.
b. What does it mean if the football and soccer ball have the same constant speed? Be descriptive, and
reference the specific quantities involved.
5. Suppose we want to rank the following objects in order from fastest to slowest. Assume each object is traveling
at a constant speed (but not necessarily the same constant speed).
Dog: 22 feet in 2 seconds
Bird: 3.3 feet in 0.5 seconds
Baseball: 61 feet in 7 seconds
Motorcycle: 190 feet in 10 seconds
Soccer Ball: 2.64 feet in 0.2 seconds
a. Why is it difficult to compare the objects’ speeds based on the information given?
b. What strategy can we use to help us complete the task?
c. Rank the objects in order from fastest to slowest.
6. Suppose we want to rank the following objects in order from fastest to slowest. Assume each object is travelling
at a constant speed (but not necessarily the same constant speed).
Bike: 88 feet in 6 seconds
Car: 70.4 feet in 4 seconds
Duck: 7.2 feet in 0.6 seconds
Cat: 13.2 feet in 1.5 seconds
Runner: 109 feet in 15 seconds
a. Why is it difficult to compare the objects’ speeds based on the information given?
b. What strategy can we use to help us complete the task?
c. Rank the objects in order from fastest to slowest.
7. What are the benefits of stating speeds in terms of distance traveled in one unit of time, such as 34 mph (34
miles traveled in one hour), 14 m/s (14 meters traveled in one second), and so on?
8. Suppose that Mary is jogging at a constant speed on 0.10 miles per minute. Let d represent the total distance (in
miles) Mary has traveled during her jog and let t represent the total number of minutes she’s been jogging.
a. Use Δ notation to represent a 6-minute time period during Mary’s jog.
b. How far does Mary travel during this 6-minute time period? Represent you answer using Δ notation.
c. Repeat parts (a) and (b) if instead of a 6-minute time period we look at a
i. 8.2-minute time period
ii. 1.6-minute time period
iii. Any x-minute time period
d. For any change in t, what happens to the change in d? Explain, then represent your thinking using Δ
notation
9. Suppose that Will is driving at a constant speed of 48 miles per hour. Let d represent the total distance (in miles)
Will has traveled during his drive and let t represent the total number of hours he’s been driving.
a. Use Δ notation to represent a 2-hour time period during Will’s drive.
b. How far does Will travel during his 2-hour time period? Represent your answer using Δ notation.
c. Repeat parts (a) and (b) if instead of a 2-hour time period we look at a
i. 3.1-hour time period
ii. 0.3-hour time period
iii. Any x-hour time period
d. For any change in t, what happens to the change in d? Explain, then represent your thinking using Δ
notation.
10. If we know that the total cost of purchasing in a bag of candy increases at a rate of $9 per pound, then it’s easy
to determine the change in total cost if we change the amount of candy we purchase. Let c represent the total
cost of purchasing candy (in dollars) and let w represent the weight of the candy purchased (in pounds).
a. Suppose we have some candy in a bag and we add 2 more pounds of candy to the bag. Represent the
change in the number of pounds of candy using Δ notation.
b. How much does the total cost of the candy we purchase change? Represent your answer using Δ
notation.
c. Repeat parts (a) and (b) if instead of adding 2 more pounds of candy we
i. Add 1.7 pounds of candy to the bag.
ii. Add 0.45 pounds of candy to the bag.
iii. Remove 1.2 pounds of candy from the bag.
d. For any change in w, what happens to the change in c? Explain, then represent your thinking using Δ
notation.
e. If your friend gives you $13 to purchase more candy, how many additional pounds of candy would you
add to your bag?
11. If we know that the total cost of purchasing a trail mix increases at a rate of $6 per pound, then it’s easy to
determine the change in total cost if we change the amount of trail mix we purchase. Let c represent the total
cost of purchasing trail mix (in dollars) and let w represent the weight of trail mix purchased (in pounds).
a. Suppose we have some trail mix in a bag and we add 4 more pounds of trail mix to the bag. Represent
the change in the number of pounds of trail mix using Δ notation.
b. How much does the total cost of the trail mix we purchase change? Represent your answer using Δ
notation.
c. Repeat parts (a) and (b) if instead of adding 4 more pounds of trail mix we
i. Add 4.2 pounds of trail mix to the bag.
ii. Remove 2.9 pounds of trail mix from the bag.
d. For any change in w, what happens to the change in c? Explain, then represent your thinking using Δ
notation.
e. If your friend gives you $15 to purchase more trail mix, how many additional pounds of trail mix would
you add to your bag?
12. Suppose we have a partially filled pitcher of water and that we want to add more water to the pitcher. We
know htat adding 60 ounces of water to the pitcher will increase the height of water in the pitcher by 7.8 inchers
and that these two quantities are related by a constant rate of change. Define variables to represent the
quantities in this context and then represent the relationship described using Δ notation.
13. Suppose we want to add some water to a bathtub, and that we know 5-gallons of water weighs 41.7 pounds.
Define variables to represent the quantities in this context and then represent the relationship described using Δ
notation.