SOLUTION: Jan works due north of home. her husband Alan works due east. They leave for work at the same time. By the time Jane is 7 miles from hom, the distance between them is one mile m

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Question 323390: Jan works due north of home. her husband Alan works due east. They leave for work at the same time. By the time Jane is 7 miles from hom, 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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: Jan works due north of home. her husband Alan works due east.
They leave for work at the same time.
By the time Jane 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?
:
This is a right triangle problem. c^2 = a^2 + b^2
Let b = 7 mi (Jan's distance from home)
Let a = the east leg (Alan's distance from home
(a+1) = c (hypotenuse, distance between them)
:
(a+1)^2 = a^2 + 7^2
FOIL (a+1)(a+1)
a^2 + 2a + 1 = a^2 + 49
Combine like terms
a^2 - a^2 + 2a = 49 - 1
2a = 48
a = 48%2F2
a = 24 mi, Alan's dist from home
:
:
Check on a calc enter: sqrt%2824%5E2+%2B+7%5E2%29 results; 25