SOLUTION: REPOST: Ride the peaks. Smith bicycled 45 miles going east from Durango, and Jones bicycled 70 miles. Jones averaged 5 miles per hour more than Smith, and his trip took one-half ho

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: REPOST: Ride the peaks. Smith bicycled 45 miles going east from Durango, and Jones bicycled 70 miles. Jones averaged 5 miles per hour more than Smith, and his trip took one-half ho      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 47290: REPOST: Ride the peaks. Smith bicycled 45 miles going east from Durango, and Jones bicycled 70 miles. Jones averaged 5 miles per hour more than Smith, and his trip took one-half hour longer than Smith’s. How fast was each one traveling?
Answer by 303795(602) About Me  (Show Source):
You can put this solution on YOUR website!
If Smith's speed is x then Jones speed is x+5.
The time taken by Smith is 45/x and the time taken by Jones is 70/(x+5). Jones time is 0.5 hour long than Smith so
45%2Fx%2B0.5=70%2F%28x%2B5%29
Multiply through by x to get
45%2B0.5x=70x%2F%28x%2B5%29
Multiply through by (x+5)
45%28x%2B5%29%2B0.5x%28x%2B5%29=70x
45x%2B225%2B0.5x%5E2%2B2.5x=70x
0.5x%5E2%2B47.5x%2B225=70x
0.5x%5E2-22.5x%2B225=0
x%5E2-45x%2B450=0
%28x-15%29%28x-30%29=0
So Smith's speed is either 15 miles per hour or 30 miles per hour. Jones speed will therefore be 20 miles per hour or 35 miles per hour.
At the slower speed Smith takes 3.0 hours and Jones takes 3.5 hours while at the faster speed Smith takes 1.5 hours and Jones takes 2.0 hours.