SOLUTION: Tommy and Zach are starting out at the same position. Tommy runs north at 3 miles per hour and Zach starts to run east 2 hours later at the rate of 4 miles per hour. How long until

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Tommy and Zach are starting out at the same position. Tommy runs north at 3 miles per hour and Zach starts to run east 2 hours later at the rate of 4 miles per hour. How long until      Log On


   

Question 1075031: Tommy and Zach are starting out at the same position. Tommy runs north at 3 miles per hour and Zach starts to run east 2 hours later at the rate of 4 miles per hour. How long until Tommy and Zach are 8 miles apart?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Tommy's head start in miles is:
+3%2A2+=+6+ mi
Let +t+ = the time that they both spend
running starting when Zach starts and ending
when they are +8+ mi apart
-------------------------------------------
Tommy's distance:
+6+%2B+3t+
Zach's distance:
+4t+
-------------------------
using Pythagorean theorem:
+%28+6+%2B+3t+%29%5E2+%2B+%28+4t+%29%5E2+=+8%5E2+
+36+%2B+36t+%2B+9t%5E2+%2B+16t%5E2+=+64+
+25t%5E2+%2B+36t++-+28+=+0+
Use quadratic formula
+t+=+%28+-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
+a+=+25+
+b+=+36+
+c+=+-28+
+t+=+%28+-36+%2B-+sqrt%28+36%5E2+-+4%2A25%2A%28-28%29+%29%29%2F%282%2A25%29+
+t+=+%28+-36+%2B-+sqrt%28+1296+%2B+2800+%29%29%2F50+
+t+=+%28+-36+%2B-+sqrt%28+4096+%29%29%2F50+
+t+=+%28+-36+%2B+64%29%2F50+
+t+=+28%2F50+
+t+=+.56+ hrs
convert to min
+t+=+.56%2A60+
+t+=+33.6+
They will be 8 mi apart in 33.6 min
-----------------------------------
check:
+%28+6+%2B+3t+%29%5E2+%2B+%28+4t+%29%5E2+=+8%5E2+
+%28+6+%2B+3%2A.56+%29%5E2+%2B+%28+4%2A.56+%29%5E2+=+8%5E2+
+%28+6+%2B+1.68+%29%5E2+%2B+2.24%5E2+=+64+
+7.68%5E2+%2B+2.24%5E2+=+64+
+58.9824+%2B+5.0176+=+64+
+64+=+64+
OK