Question 486932
Lafe is in his 4*4 300 miles due east of a car driven by shannell and is traveling due west at 30 mph. 
Shannell is speeding at 60 mph due north.
 At what time are they closest to each other. 
:
let x = travel time of both vehicles
:
This is right triangle problem c = {{{sqrt(a^2 + b^2)}}}, where
c = distance between the cars
a = 60t, 4by4 travel distance
b = (300-30t) travel distance from a point due south of the 4by4
:
The easiest way to solve this enter/plot this equation in your Ti83 or equiv
y = {{{sqrt(60x + (300-30x)^2)}}}
looks like this
:
{{{ graph( 300, 200, -4, 10, -200, 500, ((60x)^2+(300-30x)^2)^(1/2)) }}}
where distance between the cars are on the y axis and the time in hrs on the x axis. Actual minimum (from my Ti83) x = 2 hrs, y ~ 268 mi