SOLUTION: Smith travels 45 miles going East from the center of the town and Jones travels 70 miles going West from the same point. If Jones averages 5 miles per hour more than Smith and his

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Question 209401: Smith travels 45 miles going East from the center of the town and Jones travels 70 miles going West from the same point. If Jones averages 5 miles per hour more than Smith and his trip took ½ hour longer than Smith’s. How fast was each of them traveling?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Smith travels 45 miles going East from the center of the town and Jones travels
70 miles going West from the same point.
If Jones averages 5 miles per hour more than Smith and his trip took ½ hour
longer than Smith’s.
How fast was each of them traveling?
:
Let s = Smith's speed
then
(s+5) = Jones speed
:
Write a time equation: Time = dist%2Fspeed
:
Jones time = Smith's time + half hour
70%2F%28s%2B5%29 = 45%2Fs + 1%2F2
Multiply equation by 2s(s+5), results
2s(70) = 45(2(s+5)) + s(s+5)
:
140s = 90s + 450 + s^2 + 5s
:
Arrange as a quadratic equation
0 = -140s + 90s + 5s + 450 + s^2
:
s^2 - 45s + 450 = 0
:
Factors to
(s-30)(s-15) = 0
:
Two valid solutions
s = 30 mph
s = 15 mph
:
;
Check solution using 15 mph
70%2F20 = 45%2F15 + 1%2F2
3.5 = 3 + .5
:
You can check it using s = 30 mph