Sun, a kayaker, paddles 8 miles upstream (against the current) in 2 hours. Returning to her original location, she paddles downstream (with the current) the same distance in 1 hour. The equations represent x , the paddling speed, and y , the speed of the current. 2 times open paren x minus y close paren is equal to a b times open paren x plus y close paren is equal to 8 Which are true? Choose two correct answers.
Upstream, Sun’s speed over the ground is 8 ÷ 2 = 4 miles per hour, so x − y = 4. Thus 2(x − y) = 2 × 4 = 8, which means a = 8. Downstream, her speed is 8 ÷ 1 = 8 miles per hour, so x + y = 8; therefore b(x + y) = 8 requires b = 1. The true statements are “a is equal to 8” and “b is equal to 1.”
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