SOLUTION: Find the rate of two cars traveling in the same direction if they leave the same place at the same. The rate of one is twice as fast as the other, and after 4 hours the faster car

Algebra ->  Expressions-with-variables -> SOLUTION: Find the rate of two cars traveling in the same direction if they leave the same place at the same. The rate of one is twice as fast as the other, and after 4 hours the faster car      Log On


   



Question 69722: Find the rate of two cars traveling in the same direction if they leave the same place at the same. The rate of one is twice as fast as the other, and after 4 hours the faster car is 80 miles ahead of the slower car.
Formula for solving motion problems is rt=d

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
I like to use subscripts with these kind of problems
d%5B1%5D+=+r%5B1%5D%2At
d%5B2%5D+=+r%5B2%5D%2At
time will be common to both equations (4 hours)
The problems says
d%5B2%5D+=+d%5B1%5D+%2B+80 at t = 4
and
r%5B2%5D+=+2%2Ar%5B1%5D
continuing
d%5B1%5D+=+r%5B1%5D%2A4
d%5B1%5D+%2B+80+=+2%2Ar%5B1%5D%2A4
substituting
r%5B1%5D%2A4+%2B+80+=+8%2Ar%5B1%5D
4%2Ar%5B1%5D+=+80
r%5B1%5D+=+20 mi/hr answer
r%5B2%5D+=+40 mi/hr answer
d%5B1%5D+=+80 mi
d%5B2%5D+=+160 mi