SOLUTION: Please help me, I don't know how to set this up: Smith traveld 45 miles. Jones traveled 70 miles. Jones averaged 5 miles per hour more than Smith and his trip took 1/2 hour longer

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Question 36623: Please help me, I don't know how to set this up:
Smith traveld 45 miles. Jones traveled 70 miles. Jones averaged 5 miles per hour more than Smith and his trip took 1/2 hour longer than Smith's. How fast was each one traveling?
Answer by Paul(988) About Me  (Show Source):
You can put this solution on YOUR website!
Jones travelled at x+5
Simth travelled at x
TIME (of distance 2) = DISTANCE/SPEED1 - DISTANCE/SPEED2
Equation:
45%2Fx-70%2F%28x%2B5%29=1%2F2
 -->Cross multiply:

45%28x%2B5%29-70%28x%29=%28%28x%29%28x%2B5%29%29%2F2

225-25x=%28x%5E2%2B5x%29%2F2

450-50x=x%5E2%2B5x

x%5E2%2B55x-450=0

SOlve that you get x=7 (rounded)

7+5=12

Hence, Simth travelled at 7mph and Jones travelled at 12mph.

Paul.