<PRE><B>Question 480990</B>
Two cruise ships leave port at the same time.
One heads south and the other goes east.
 Later that day they are 170 miles apart.
 One ship has traveled 70 miles more than the other ship.
 How many miles has each ship gone? 
:
Time is not a factor here, so the dist formula is not used.
:
Let x = the distance traveled by the 1st ship
then
(x+70) = the distance traveled by 2nd ship
:
This a right angle problem where a^2 + b^2 = c^2:
one leg (a) = x
2nd leg (b) = (x+70)
hypotenuse (c) = dist between the ships (170mi)
:
x^2 + (x+70)^2 = 170^2
x^2 + x^2 + 140x + 4900 = 28900
2x^2 + 140x + 4900 - 28900 = 0
2x^2 + 140x - 24000 = 0
Simplify, divide by 2
x^2 + 70x - 12000 = 0
You can use the quadratic formula a=1, b=70, c=-12000, but it will factor to
(x+150)(x-80) = 0
the positive solution
x = 80 mi traveled by the 1st ship
then
80 + 70 = 150 mi traveled by the 2nd ship
:
:
Check this on your calc; enter: {{{sqrt(80^2 + 150^2)}}}, results 170</PRE>