SOLUTION: At noon, car A is 41 miles due west of car B and traveling east at a constant speed of 55 miles an hour. Meanwhile, car B is traveling north at 40 miles per hour. At what time will

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: At noon, car A is 41 miles due west of car B and traveling east at a constant speed of 55 miles an hour. Meanwhile, car B is traveling north at 40 miles per hour. At what time will      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 606591: At noon, car A is 41 miles due west of car B and traveling east at a constant speed of 55 miles an hour. Meanwhile, car B is traveling north at 40 miles per hour. At what time will the two cars be closest to each other? Suggestion, minimize the square of the distance, rather than the distance itself
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
At noon, car A is 41 miles due west of car B and traveling east at a constant speed of 55 miles an hour.
Meanwhile, car B is traveling north at 40 miles per hour.
At what time will the two cars be closest to each other?
:
the relationship between the two cars form a right triangle where
a = (41-55t), car a distance from reference point
b = 40t, car B travel distance from the the same point
c = distance between the cars at t time
:
c^2 = (41-55t)^2 + (40t)^2
c^2 = 1681 - 4510t + 3025t^2 + 1600t^2
c^2 = 4625t^2 - 4510t + 1681
c = sqrt%284625t%5E2+-+4510t+%2B+1681%29
Plot this equation
+graph%28+300%2C+200%2C+-.5%2C+2%2C+-5%2C+50%2C+sqrt%284625x%5E2+-+4510x+%2B+1681%29%29+
looks like they will closest together in half an hour, about 24 miles