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Question 206941: two boats travel at right angles to each other after leaving a dock at the same time. one hour later they are 25 miles apart. if one boat travels 5 miles per hour faster than the other, what is the rate of each?(Hint: use the pythagorean theorem).
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! two boats travel at right angles to each other after leaving a dock at the same time. one hour later they are 25 miles apart. if one boat travels 5 miles per hour faster than the other, what is the rate of each?
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Draw the picture labeling the hypotenuse of the rt. triangle as 25,
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Slower boat DATA:
rate = x mph ; time = 1 hr. ;distance = rt = x miles
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Faster boat DATA:
rate = x+5 mph ; time = 1 hr. ; distance = rt = x+5 miles
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Label the legs of the rt. triangle as "x" and "x+5"
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Use Pythagoras to solve for "x":
x^2 + (x+5)^2 = 25^2
2x^2 + 10x + 25 = 625
2x^2 + 10x - 600 = 0
x^2 + 5x - 300 = 0
(x+20)(x-15) = 0
Positive solution:
x = 15 mph (rate of the slower boat)
x+5 = 20 mph (rate of the faster boat)
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Cheers,
Stan H.
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