SOLUTION: Can someone help me solve this? Type of Problem: Applications of Linear Systems Solve the problem by using a system of equations. A Porsche and a VW Bug that were 450 miles ap

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: Can someone help me solve this? Type of Problem: Applications of Linear Systems Solve the problem by using a system of equations. A Porsche and a VW Bug that were 450 miles ap      Log On


   

Question 791157: Can someone help me solve this?
Type of Problem: Applications of Linear Systems
Solve the problem by using a system of equations.
A Porsche and a VW Bug that were 450 miles apart traveled toward each other. They met after 5 hours. If one car can travel twice as fast as the other car, what were their speeds?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Slow speed, r
Fast speed, 2r
r*t=d

Total time was 5 hours, so t=d/r and the other time would be d/(2r).
?
The amount of time, x, is the same for both cars.

CAR1___________r____________x__________rx
CAR2___________2r___________x__________2rx
Total______________________ 5__________450


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SYSTEM OF EQUATIONS:
x%2Bx=5 and rx%2B2rx=450
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2x=5 and rx%2B2rx=450
x=5%2F2 and x%28r%2B2r%29=450
Substitution for x gives %285%2F2%29%283r%29=450
15r%2F2=450
r=450%282%2F15%29
highlight%28r=60%29 for the slow car
Fast car is highlight%28120%29 mph