SOLUTION: Smith bicycled 45 miles going east from Dursango, and Jones bicycled 70 miles. jones averaged 5 miles per hour more than smith, and his trip took one-half hour longerthan smith's.

Question 265733: Smith bicycled 45 miles going east from Dursango, and Jones bicycled 70 miles. jones averaged 5 miles per hour more than smith, and his trip took one-half hour longerthan smith's. How fast was each one traveling?
this is what i have..
45x=70(x+5)
45x=70x+350
-350=70x-45x
-350=25x
x=-14
45/14= 3.2mph & 70/14+5=10mph?
Answer by palanisamy(496) (Show Source): You can put this solution on YOUR website!
Let the speed of Smith = x mph
Then, the speed of Jones = x+5
Given, Smith bicycled 45 miles going east from Dursango, and Jones bicycled 70 miles.
Time = Distance/speed.
Time taken by Smith = 45/x
Time taken by Jones = 70/(x+5)
Gien, Jone's trip took one-half hour longerthan smith's.
70/(x+5) = 45/x + 1/2
70/(x+5) = 45/x+1/2
70/(x+5) = (90+x)/2x
140x = (90+x)(x+5)
140x = 90x+450+x^2+5x
0 = x^2-45x+450
x^2-45x+450 = 0
(x-30)(x-15) = 0
x = 30 or 15
Therefore the speed of Smith = 30 mph and Then, the speed of Jones =35 mph
or the speed of Smith = 15 mph and the speed of Jones = 20 mph

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