SOLUTION: Precalculus Michael Sullivan Section 1.1 Q. 67 A Ford Focus and a Freightliner truck leave an intersection at the same time. The Focus heads due east at an average speed o

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: Precalculus Michael Sullivan Section 1.1 Q. 67 A Ford Focus and a Freightliner truck leave an intersection at the same time. The Focus heads due east at an average speed o      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 1210651: Precalculus
Michael Sullivan
Section 1.1
Q. 67
A Ford Focus and a Freightliner truck leave an intersection at the same time.
The Focus heads due east at an average speed of 30 mph, while the truck heads due south at an average speed of 40 mph. Find an expression for their distance apart d (in miles) at the end of t hours.
Answer by ikleyn(53942) About Me  (Show Source):
You can put this solution on YOUR website!
Precalculus
Michael Sullivan
Section 1.1
Q. 67
A Ford Focus and a Freightliner truck leave an intersection at the same time.
The Focus heads due east at an average speed of 30 mph, while the truck heads due south at an average speed of 40 mph.
Find an expression for their distance apart d (in miles) at the end of t hours.
~~~~~~~~~~~~~~~~~~~~~~~~~~ 


This problem is for 2D space (x,y).


At the end of t hours, the Ford Focus car is on x-axis, having x-coordinate x(t) = 30t miles and y-coordinate 0.


At the same time moment, the Freightliner truck is on y-axis, having y-coordinate y(t) = -40t miles and x-coordinate 0.


To find the expression for the distance apart d, use the distance formula

    d = sqrt(x^2(t) + y^2(t)) = sqrt%28%2830t%29%5E2+%2B+%28-40t%29%5E2%29%29 = sqrt%28900t%5E2+%2B+1600t%5E2%29 = sqrt%282500t%5E2%29 = 50t miles.


At this point, the problem is solved completely and the expression for the distance is obtained.


ANWER.  d(t) = 50t miles, where t is in hours.

Solved.