Question 510833
plane A is 40 miles south and 100 miles east of plane B. plane A is flying 2 miles west for ever mile it flies north, while plane B is flying 3 miles east for every mile it flies south. where do there paths cross?
:
Write a linear equation for the line taken by each plane
With O origin, 
Plane B: When x = 0, y = 40
"plane B is flying 3 miles east for every mile it flies south."
Using the rise/run rule the slope will be -1/3 (negative because it's moving southward)
y = -{{{1/3}}}x + 40
{{{ graph( 300, 200, -20, 130, -10, 60, -.333x+40) }}}
:
Plane A: x intercept = +100, find the y intercept
"plane A is flying 2 miles west for ever mile it flies north,"
Slope = -1/2; find the y intercept (b)
{{{-1/2}}}(100) + b = 0
-50 + b = 0
b = 50
the equation for A: y = -{{{1/2}}}x + 50, plot this with B
intercept x=60 mi east, y=20 mi north
{{{ graph( 300, 200, -20, 130, -10, 60, -.333x+40, -.5x+50) }}}