SOLUTION: Rosa works due north of home. Her husband Alan works due East. They leave for work at the same time. By the time Rosa is 3 miles from home, the distance between them is one mile mo

Algebra ->  Equations -> SOLUTION: Rosa works due north of home. Her husband Alan works due East. They leave for work at the same time. By the time Rosa is 3 miles from home, the distance between them is one mile mo      Log On


   

Question 1002409: Rosa works due north of home. Her husband Alan works due East. They leave for work at the same time. By the time Rosa is 3 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 ankor@dixie-net.com(22740) About Me  (Show Source):
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Rosa works due north of home. Her husband Alan works due East.
They leave for work at the same time.
By the time Rosa is 3 miles from home, the distance between them is one mile more than Alan's distance from home.
How far from home is Alan?
:
This is a Pythagoras problem. the distance between them is the hypotenuse
a^2 + b^2 = c^2
:
a = Alan's distance from home
b = 3 mi
c = (a+1); one more mile than Alan's dist
:
a^2 + 3^2 = (a+1)^2
FOIL (a+1)(a+1)
a^2 + 9 = a^2 + 2a + 1
a^2 - a^2 + 9 - 1 = 2a
8 = 2a
a = 4 mi is Alan from home
:
:
Check 4^2 + 3^2 = 5^2