Notes
Example 1: In Example 4, suppose it takes the kayakers 5 hours to travel 10 miles upstream and 2 hours to travel 10
miles downstream. The speed of the current remains constant during the trip. Find the average speed of the kayak in
still water and the speed of the current.
Step 1: Write a system of equations. First find the speed of the kayak going upstream and the speed of the kayak
going downstream.
Upstream:
d = rt
Downstream: d = rt
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__________________
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__________________
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Equation 1: Going upstream
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Equation 2: Going downstream
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Step 2: Solve the system of equations.
The average speed of the kayak in still water is __________________ and the speed of the current is _____________.
______________________________________________________________________________________________
Practice Problems
1. A riverboat travels 28 miles upstream in 7 hours. It travels 28 miles downstream in 5 hours. The speed of the
current remains the same during the travel upstream and downstream. Find the average speed of the riverboat in
still water and the speed of the current.
2. ROWING During a practice, a 4 person crew team rows a rowing shell upstream (against the current) and then
rows the same distance downstream (with the current). The shell moves upstream at a speed of 4.3 meters per
second and downstream at a speed of 4.9 meters per second. The speed of the current remains constant. Write
and solve a system of equations to find the average speed of the shell in still water and the speed of the current.
3. pg. 450: #43
Example 2: A food corporative is a business that usually offers special prices on locally grown food and produce.
Some cooperatives are clubs and other are retail stores. The weekly costs for seasonal produce offered by a clubbased and a store- based food cooperative are shown in the table. Find the number of weeks at which the total cost
of weekly produce will be the same.
Type of cooperative
Club fee (dollars)
Cost per week
(dollars)
Club
$20
$15
Retail
None
$17.50
Solution
Step 1: Write a system of equations. Let y be the total cost after x months
Equation 1:
Equation 2:
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Step 2: Substitute
The total cost will be the same for both cooperatives at ______ weeks.
Example 3: Laura has $4.50 in dimes and quarters. She has 3 more dimes than quarters. How many quarters does she
have?
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Practice Problems
1. pg. 440: # 31, 32, 33
2. Melissa has 36 coins in her pocket, all of which are dimes and nickels. IF she has three fewer than twice as
many nickels as dimes, how many nickels and dimes does she have?