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?
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I'll assume both were traveling in the same direction. Let's set up the following chart to gather the information:
Code:
rate time dist
Smith r t 45
Jones r+5 t+.5 70
Since the problem only asks for the rates of each, we can use the formula:
rate * time = dist
and solve for t in the Smith case. You get: t = 45/r
Use this value of t in the Jones case:
(r+5) (45/r + .5) = 70
We can solve this by multiplying both sides by r to clear the denominator to get:
45r + 225 + .5r^2 + 2.5r = 70r
Gather terms to get:
.5r^2 - 22.5r + 225 = 0
Solving this we get:
r = 15, or, r = 30
It turns out that both of these values fit the original statement of the problem. So the solutions are:
Smith: 15 mph; Jones: 20 mph [also, Smith time: 3 hrs; Jones time: 3.5 hrs]
or
Smith: 30 mph; Jones: 35 mph [also, Smith time: 1.5 hrs; Jones time: 2 hrs]
Hope that helps...
Steve
