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 is equal to rt .
Answer
A
1 point 5 is equal to 9 times x minus y 0 point 5 is equal to 9 times x plus y
B
0 point 5 is equal to 9 times open paren x minus y close paren 1 point 5 is equal to 9 times x plus y
C
9 is equal to 0 point 5 times x minus y 9 is equal to 1 point 5 times x plus y
D
9 is equal to 1 point 5 times open paren x minus y close paren 9 is equal to 0 point 5 times x plus y
Explanation
With the current, the boat’s speed is x + y, and the 30-minute trip takes 0.5 hour, so the distance equation is 9 = 0.5(x + y). Against the current, its speed is x − y, and the 90-minute trip takes 1.5 hours, giving 9 = 1.5(x − y). These equations match choice D.
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