Question 498281: Two fishing boats depart a harbor at the same time, one traveling east, the other south. The eastbound boat travels at a speed 7 mi/h faster than the southbound boat. After five hours the boats are x = 65 mi apart. Find the speed of the southbound boat.
Answer by htmentor(1343)   (Show Source):
You can put this solution on YOUR website! Two fishing boats depart a harbor at the same time, one traveling east, the other south. The eastbound boat travels at a speed 7 mi/h faster than the southbound boat. After five hours the boats are x = 65 mi apart. Find the speed of the southbound boat.
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Let s = the speed of the southbound boat
Then s+7 = the speed of the eastbound boat
The separation distance is the hypotenuse of a right triangle.
The length of the other two legs will be equal to the speed of the boat times
the travel time of the boat
The distance traveled by the eastbound boat = (s+7)*5
The distance traveled by the southbound boat = s*5
Using the Pythagorean theorem, we can write
(5(s+7))^2 + (5s)^2 = 65^2
This can be simplified to
s^2 + 7s - 60 = 0
Factoring gives
(s+12)(s-5) = 0
Take the positive solution, s = 5
So the speed of the southbound boat is 5 mph
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