Question 1014512: Mary works due north of home. Her husband works due east. They leave for work at the same time. By the time Mary is 7 miles from home, the distance between them is one mile more than Alan's distance from home. How far from home is Alan?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! she's 7 miles from home due north.
he's x miles from home due east.
the distance between them is x + 1.
you have a right triangle where one leg is 7 and one leg is x and the hypotenuse is x+1.
by pythagorus, hypotenuse squared = one leg square plus the other leg squared.
you get (x+1)^2 = 7^2 + x^2 = 49 + x^2
simplify to get x^2 + 2x + 1 = 49 + x^2
subtract x^2 from both sides of the equation to get 2x + 1 = 49
subtract 1 from both sides of this equation to get 2x = 48
divide both sides of this equation by 2 to get x = 24.
that's your solution.
alan is 24 miles from home and the distance between them is 25 miles.
once again, you have the right triangle where one leg is 7 and the other leg is 24 and the hypotenuse is 25.
7^2 + 24^2 is equal to 49 + 576 which is equal to 625.
this confirms the pythagrus rule has been calculated successfully.
since 25 is equal to 24 + 1, then the solution is confirmed as good because all requirements of the problem have been satisfied.
your solution is that her husband is 24 miles from home.
she is 7 miles from home due north.
he is 24 miles from home due east.
they are 25 miles apart.
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