Problem in description. Thanks :)

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, North Carolina. A boat travels with the current 110mi

 from Miami, Florida, to Freeport, Bahamas, in 2.5hr

. The return trip against the same current takes 323

 hr

. Find the speed of the boat in still water and the speed of the current.

Answer 1

Well, it must be one strong current, or the numbers are not copied into this problem correctly. However, it can still be easily solved. Let C = speed of the current (mi/h) and B = speed of Boat (mi/hr). Since the trip to the Bahama's took the shortest time we set the positive direction of the current C towards Bahamas. Therefore:

110 = 2.5(B+C)

Since return trip is same distance, but current is not fighting against boat, we make C negative or

110 = 323(B-C)

Because the trip distances are the same, the equations both = 110 so

2.5(B+C) = 323(B-C)

2.5B + 2.5C = 323B -323C

325.5C = 320.5B

C = 320.5B/325.5

Then take C and sub into either equation. I selected first

110 = 2.5(B+C)

110 = 2.5(B+320.5B/325.5)

110 = 2.5(1.98464B)

110 = 4.96B

B = 22.17 mph

So solve for C, plug B back into either equation. I came up with 21.89 mph for the current.