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?
:
Let s = Smith's speed
then
(s+5) = Jones speed
:
Write a time equation: Time = {{{dist/speed}}}
:
Jones time = Smith's time + half hour
{{{70/(s+5)}}} = {{{45/s}}} + {{{1/2}}}
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
{{{70/20}}} = {{{45/15}}} + {{{1/2}}}
3.5 = 3 + .5
:
You can check it using s = 30 mph