SOLUTION: When driving a 9 hour trip home, Sharon drove 420 miles on the interstate and 135 miles on country roads. Her speed on the interstate was 25 more than on country roads. What was he

Question 1136208: When driving a 9 hour trip home, Sharon drove 420 miles on the interstate and 135 miles on country roads. Her speed on the interstate was 25 more than on country roads. What was her speed, in miles per hour , on country roads?
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39620)   (Show Source): You can put this solution on YOUR website!

SPEED TIME DISTANCE INTERST r+25 420/(r+25) 420 COUNTRY r 135/r 135 TOTAL 9

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Answer by ikleyn(52812)   (Show Source): You can put this solution on YOUR website!
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Let r = her speed, in miles per hour , on country roads. Then the other speed is (r+25) mph. You have this "time" equation + = 9 hours. <<<---=== Every fraction on the left side is the time to cover the distance . . . To solve it, multiply both sides by r*(r+25). 420r + 135*(r+25) = 9r*(r+25). Now simplify and solve this quadratic equation. 420r + 135r + 135*25 = 9r^2 + 9*25r 9r^2 - 330r - 3375 = 0 3r^2 - 110r - 1125 = 0 r = = . Only positive root is meaningful r = = = 45. ANSWER. 45 miles per hour. CHECK. + = + = 6 + 3 = 9 hours. ! Correct !

Solved.

Using "time" equation is the STANDARD way to solve such problems.

From this solution, learn on how to write, how to use and how to solve a "time" equation.

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To see many other similar solved problems, look into the lessons
    - Had a car move faster it would arrive sooner
    - How far do you live from school?
in this site.

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