Question 1014512
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.