3
QuizMultiple Choice

Modeling with Systems of Linear Equations

Question 3 • (OC27) MATH COLL ALGEBRA-1200710-S1-Degele-VOL7006P

A motorboat travels 9 miles downstream (with the current) in 30 minutes. The return trip upstream (against the current) takes 90 minutes.Which system of equations can be used to find x, the speed of the boat in miles per hour, and y, the speed of the current in miles per hour? Recall the formula d = rt.

Answer
A
9 = 0.5(x – y) 9 = 1.5(x + y)
B
9 = 1.5(x – y) 9 = 0.5(x + y)
C
0.5 = 9(x – y) 1.5 = 9(x + y)
D
1.5 = 9(x – y) 0.5 = 9(x + y)

Explanation

Downstream, the boat’s speed is x + y because the current helps it, and 30 minutes is 0.5 hour. Using distance = rate × time gives 9 = 0.5(x + y). Upstream, the speed is x − y and 90 minutes is 1.5 hours, so 9 = 1.5(x − y). These equations match choice B.

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