<PRE><B>Question 165413</B>
Two ships leave port, one sailing east and the other south. Some time later they are 17 mi apart, with the eastbound ship 7 mi farther from port than the southbound ship. How far is each from port?
:
This is a right triangle problem
:
Let x = distance from port of the southbound ship (one side of a right triangle)
then
(x+7) = distance from port of the eastbound ship (2nd side of a right triangle)
:
Distance between them = 17 mi (hypotenuse of the triangle)
:
x^2 + (x+7)^2 = 17^2
:
x^2 + x^2 + 14x + 49 = 289
:
2x^2 + 14x + 49 - 289 = 0
:
2x^2 + 14x - 240 = 0
Simplify, divide equation by 2
x^2 + 7x - 120 = 0
Factor
(x-8)(x-15) = 0
Positive solution
x = 8 distance from port of the southbound ship
and
8 + 7 = 15 mi distance of the eastbound ship
:
:
Check on calc enter: sqrt(8^2+15^2) = 17</PRE>