SOLUTION: David and Amy start at the same point and begin biking in different directions. David is biking west at a speed of 17 miles per hour. Amy is biking south at a speed of 15 miles per
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Question 1147349: David and Amy start at the same point and begin biking in different directions. David is biking west at a speed of 17 miles per hour. Amy is biking south at a speed of 15 miles per hour. After how many hours will they be exactly 23 miles apart? Round your answer to two decimal places.
I have tried setting it up as 15x+17x=23 (my answer was 0.72 and it was wrong). Found 3 solutions by Alan3354, josgarithmetic, greenestamps:Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website! David and Amy start at the same point and begin biking in different directions. David is biking west at a speed of 17 miles per hour. Amy is biking south at a speed of 15 miles per hour. After how many hours will they be exactly 23 miles apart? Round your answer to two decimal places.
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It's a right triangle, and 23 miles is the hypotenuse.
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t = time in hours
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(17t)^2 + (15t)^2 = 23^2
289t^2 + 225t^2 = 529
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Solve for t
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Odd that it says "exactly 23 miles" then says round to 2 places.
15x+17x=23 would be a valid equation if the two of them were biking in opposite directions, like east and west, or north and south.
But they are biking in directions that differ by 90 degrees.
That means the paths of the two of them, along with the distance between them, form a right triangle. The distances the two travel (your 15x and 17x) are the legs; the distance between them is the hypotenuse.
Then you can use the Pythagorean Theorem to find when the distance between them will be 23 miles:
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