SOLUTION: Smith bicycled 45 miles going east form 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.

Question 58994This question is from textbook Elementry and Intermediate Algerbra
: Smith bicycled 45 miles going east form 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?This question is from textbook Elementry and Intermediate Algerbra

Answer by stanbon(48552) (Show Source):
You can put this solution on YOUR website!
Smith bicycled 45 miles going east form 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?
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Smith DATA:
distance = 45 mi ; rate = x mph ; time = d/r = 45/x hrs.
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Jones DATA:
distance = 70 mi ; rate = (x+5)mph ; time = d/r = 70/(x+5)
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EQUATION:
Jones time-Smith time = 1/2 hr
70/(x+5) - (45/x) = 1/2
140x - 90(x+5)= x(x+5)
140x-90x-450 = x^2+5x
x^2-45x+450=0
x=[45+-sqrt(225)]/2
x=[45+15]/2 =30
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Smith's rate was 30 mph
Jones rate was x+5 = 35 mph
Cheers,
Stan H.