SOLUTION: Tommy and Zach are starting out at the same position. Tommy runs north at 5 miles per hour and Zach starts to run east 2 hours later at the rate of 8 miles per hour. How long until

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Tommy and Zach are starting out at the same position. Tommy runs north at 5 miles per hour and Zach starts to run east 2 hours later at the rate of 8 miles per hour. How long until      Log On


   

Question 1077979: Tommy and Zach are starting out at the same position. Tommy runs north at 5 miles per hour and Zach starts to run east 2 hours later at the rate of 8 miles per hour. How long until Tommy and Zach are 16 miles apart? Round to the nearest tenth if necessary.

Answer by jorel1380(3719) About Me  (Show Source):
You can put this solution on YOUR website!
Tommy has a head start of 5 x 2, or 10 miles.Then Zach runs at 8 mph. Let x be the amount of time Zach runs. Then:
(10+5x)²+(8x)²=16²
100+100x+25x²+64x²=256
89x²+100x-156=0
(89x-78)(x+2)=0
x=-2 or 78/89
We get a positive value of 78/89, or 0.8764 hours before they are 16 miles apart. ☺☺☺☺