Micah rows his boat on a river 4.48 miles downstream, with the current , 0.32 hours. He rows back upstream the same distance, against the current , 0.56 hours . Assuming his rowing speed of the cure are constant, what is the spend of the current
Short Answer: Current speed = 3 miles per hour. Givens Downstream d = 4.48 miles t = 0.32 hours. c = ?? r_boat = ??
Upstream d = 4.48 miles t = 0.56 miles c = ?? r_boat =??
Equations. Since the distances are the same, you can equate the distances and come back to them later. d = r*t (r - c) * 0.56 = (r + c) * 0.32 This will give you r in terms of c. Notice the minus sign on the left. It's there because the current is going against you, slowing you down. Remove brackets 0.56r - 0.56c = 0.32r + 0.32c Add 0.56c to both sides. 0.56r = 0.32r + 0.32c + 0.56c 0.56r = 0.32r + 0.88c Subtract 0.32r from both sides. 0.56r - 0.32r = 0.88c 0.24r = 88c Divide by 0.24 r = 0.88/0.24 c r = 3 2/3 c
Now we have enough information to solve for c
4.48/(r + c) = 0.32 4.48 = 0.32 * (r + c) Substitute r = 3 2/3c into this equation. 4.48 = 0.32 * (3 2/3c + c) Add c and 3 2/3c together. 4.48 = 0.32 * (4 2/3c) Change 4 2/3 to 14/3 4.48 = 0.32 * 14/3 c 4.48 = (4.48 / 3 ) * c 4.48 = 1.493333333 c Divide 4.48 by 1.493333333 c = 4.48 / 1.4933333 c = 3 mph <<<<<<<<<<<<<<Answer
