Lesson 3.3: Modeling with Systems of Linear Equations
Question 10 • (OC27) MATH COLL ALGEBRA-1200710-S1-Degele-VOL7006P
An aircraft travels with the wind for 120 miles in 0.75 of an hour. The return trip is flown against the wind and takes exactly 1 hour.Which system of linear equations represents x, the speed of the plane in miles per hour, and y, the speed of the wind in miles per hour? Recall the formula d = rt.
Answer
A
0.75(x + y) = 120 x − y = 120
B
0.75(x − y)= 120 x + y = 120
C
120(x + y) = 0.75 120(x − y) = 1
D
120(x − y) = 0.75 120(x + y) = 1
Explanation
With the wind, the plane’s speed is x + y, so distance = rate × time gives 0.75(x + y) = 120. Against the wind, its speed is x − y and the trip takes 1 hour, giving x − y = 120; these equations are choice A.
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