SOLUTION: Smith bicycled 45 miles going east from Dallas, and Jones bicycled 70 miles. Jones avgd 5 miles per hour more than Smith and his trip took one-half hour longer than Smiths. How f

Question 125116: Smith bicycled 45 miles going east from Dallas, and Jones bicycled 70 miles. Jones avgd 5 miles per hour more than Smith and his trip took one-half hour longer than Smiths. How fast was each one traveling?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Smith bicycled 45 miles going east from Dallas, and Jones bicycled 70 miles. Jones avgd 5 miles per hour more than Smith and his trip took one-half hour longer than Smiths. How fast was each one traveling?
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Smith DATA:
Distance = 45 miles ; rate = x mph ; time = d/r = 45/x hrs.
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Jones DATA:
Distance = 70 miles ; rate = x+5 mph ; time = d/r = 70/(x+5) hrs.
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EQUATION:
Jones time - Smith time = 1/2)
70/(x+5) - 45/x = 1/2
Multiply thru by 2x(x+5) to get:
70*2x - 45*2(x+5) = x(x+5)
140x - 90x+450 = x^2+5x
x^2-45x-450 = 0
(x-15)(x-30) = 0
x = 15 or x = 30
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Reasonable answer for bicyclists:
Smith rate = 15 mph
Jones rate = 20 mph
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If you like x=30
Smith rate = 30 mph
Jones rate = 35 mph
======================
Cheers,
Stan H.
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