Question
The Gulf Stream is a warm ocean current that extends from the eastern side of the Gulf of Mexico up through the Florida Straits and along the southeastern coast of the United States to Cape Hatteras, Nort Carolina. A boat travels with the current 110 mi from Miami, Florida, to Freeport, Bahamas, in 5 hr. The return trip against the same current takes 7 6/7 hr. Find the speed of the boat in still water and the speed of the current.
Answers
Vb = velocity of boat.
Vc = velocity of current.
Downstream: (Vb+Vc) * T = 110 mi.
(Vb+Vc) * 5 = 110,
Eq1: Vb+Vc = 22 mi/h.
Upstream: (Vb-Vc) * T = 110.
(Vb-Vc) * 7 6/7 = 110,
Eq2: Vb - Vc = 14 mi/h.
Add Eq1 and Eq2:
Vb + Vc = 22.
Vb - Vc = 14
Sum : 2Vb = 36,
Vb = 18 mi/h.
In Eq1, replace Vb with 18 and solve for Vc.
Vc = velocity of current.
Downstream: (Vb+Vc) * T = 110 mi.
(Vb+Vc) * 5 = 110,
Eq1: Vb+Vc = 22 mi/h.
Upstream: (Vb-Vc) * T = 110.
(Vb-Vc) * 7 6/7 = 110,
Eq2: Vb - Vc = 14 mi/h.
Add Eq1 and Eq2:
Vb + Vc = 22.
Vb - Vc = 14
Sum : 2Vb = 36,
Vb = 18 mi/h.
In Eq1, replace Vb with 18 and solve for Vc.
I want to be sure before. I have 18 for boat still in the water and 4 speed of the current. Is that correct?
Yes, that is correct.