Speed Boat Bahamas

word problem?

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 100 mi from Miami, Florida,
to Freeport, Bahamas, in 4 hr. The return trip against the same current takes 33 1

3

hr. Find the
speed of the boat in still water and the speed of the current.
2 ANSWERS BELOW ARE INCORRECT

Let b = the speed of the boat in still water
Let c = the speed of the current
b + c = speed of boat with the current
b − c = speed of boat against the current
Distance Rate Time

With current 100 b + c 4

Against current 100 b − c 20/3

(rate)(time) = (distance)
(b + c)(4) = 100
(b − c)( 20

3
)
= 100

Divide the first equation by 4, the second equation by (20/3), add the results, and solve:
(b + c)(4) = 100 div 4

b + c = 25
(b − c) 20

3

= 100 div 20/3

b − c = 15
2b = 40
b = 20

Substitute and solve for c:
20 + c = 25
c = 5

The speed of the boat is 20 mph and the speed of the current is 5 mph.

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