Name: ____________
Chinese Name: _____________
Date: ____ - __ - __
Systems of Linear Equations Use for Mastery
Instructions
Read the problem statement below. Show all of your work on the page. Points are given for
clear solution steps, organization, and a demonstration of understanding. No talking is
allowed. You may use your calculator.
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Problem Statement
Two cars leave town at the same time and travel in opposite directions. The average rate of
speed of one car is 15 miles per hour faster than the average rate of speed of the other car.
The cars are 315 miles apart after three hours.
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Question
Find the average rate of speed of the two cars.
Solution
Let the average rate of speed of the faster car be 𝑦𝑦 miles per hour.
Let the average rate of speed of the slower car be 𝑥𝑥 miles per hour.
Substitute (1) into (2)
Solve for 𝑥𝑥
Substitute 𝑥𝑥 = 45 into (1)
𝑦𝑦 = 𝑥𝑥 + 15
(1)
3𝑥𝑥 + 3𝑦𝑦 = 315
(2)
3𝑥𝑥 + 3(𝑥𝑥 + 15) = 315
(3)
6𝑥𝑥 + 45 = 315
𝑥𝑥 = 45
𝑦𝑦 = (45) + 15
𝑦𝑦 = 60