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 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 = {{{48/2}}}
a = 24 mi, Alan's dist from home
:
:
Check on a calc enter: {{{sqrt(24^2 + 7^2)}}} results; 25