Question 6311: Problem Solving Using Systems of Equations
Julie and Eric row their boat(at a constant speed) 55 miles downstream for 5 hours, helped by the current. Row at the same rate, the trip back against the current takes 11 hours. Find the rate of the current.
Answer by Earlsdon(6294)   (Show Source):
You can put this solution on YOUR website! You can use the distance formula (d = rt) to solve this problem.
Downstream trip: d = 55 miles, t = 5 hours, and r = R + C
R + C is their rowing speed (R) plus the rate of the current (C).
Upstream trip: d = 55 miles, t = 11 hours, and r = R - C
R - C is their rowing speed (R) minus the the rate of the current (C).
Downstream: 55 mi. = (R + C)5 hrs. Divide both sides by 5: R + C = 11
Upstream: 55 mi. = (R - C)11 hrs. Divide both sides by 11: R - C = 5
R + C = 11 Subtract C from both sides.
R = 11 - C Substitute this into: R - C = 5
(11 - C) - C = 5 Simplify and solve for C
11 - 2C = 5 Add 2C to both sides.
11 = 2C + 5 Subtract 5 from both sides.
6 = 2C Divide both sides by 2
C = 3 mph is the rate of the current.
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