SOLUTION: Kristina went on a 220 mile trip to a soccer game. On the way back, due to road construction she had to drive 11 miles per hour slower. This made the trip take 1 hour longer. How f

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Kristina went on a 220 mile trip to a soccer game. On the way back, due to road construction she had to drive 11 miles per hour slower. This made the trip take 1 hour longer. How f      Log On


   

Question 1149181: Kristina went on a 220 mile trip to a soccer game. On the way back, due to road construction she had to drive 11 miles per hour slower. This made the trip take 1 hour longer. How fast did she drive to the soccer game?
Found 3 solutions by josgarithmetic, ikleyn, VFBundy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
                    SPEED       TIME         DISTANCE
GOING                r          220/r          220

RETURN              r-11        220/(r-11)     220

DIFFERENCE                       1

220%2F%28r-11%29-220%2Fr=1
Solve for r.

Answer by ikleyn(52777) About Me  (Show Source):
You can put this solution on YOUR website!
.

Let "x" be the average rate driving "to there", in miles per hour.


The "time" equation is


    220%2F%28x-11%29 - 220%2Fx = 1


The first fraction on the left side is the time driving back;  the second fraction on the left is the time driving "to there";

the "1" on the right side is the given difference of the times.



Simplify the "time" equation step by step and solve for x:


    220*x - 220*(x-11) = x*(x-11)

    11*220            = x^2 - 11x

    x^2 - 11x - 2420 = 0

    x%5B1%2C2%5D = %2811+%2B-+sqrt%2811%5E2+%2B+4%2A2420%29%29%2F2 = %2811+%2B-+99%29%2F2.


Only positive root makes sense


    x = %2811+%2B+99%29%2F2 = 55.


ANSWER.  55 miles per hour.


CHECK.   220%2F%2855-11%29 - 220%2F55 = 220%2F44 - 220%2F55 = 5 - 4 = 1 hour.    ! Correct !

Solved.

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Using  "time"  equation is the  STANDARD  method of solving such problems.
From this lesson,  learn on how to write,  how to use and how to solve a  "time"  equation.

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?
    - Earthquake waves
    - Time equation: HOW TO use, HOW TO write and HOW TO solve it
in this site.


Answer by VFBundy(438) About Me  (Show Source):
You can put this solution on YOUR website!
To the game:
Distance = 220
Rate = r
Time = t = 220/r

From the game:
Distance = 220
Rate = r - 11
Time = t + 1 = (220/r) + 1 = 220/(r - 11)

(220/r) + 1 = 220/(r - 11)

Cross-multiply:

(r - 11)((220/r) + 1) = 220

220 + r - 2420/r - 11 = 220

209 + r - 2420/r = 220

r - 2420/r = 11

r²/r - 2420/r = 11

(r² - 2420)/r = 11

Cross-multiply:

11r = r² - 2420

r² - 11r - 2420 = 0

(r - 55)(r + 44) = 0

r = 55 and r = -44. Since the rate (r) cannot be a negative number, we are left with r = 55.

To the game:
Rate = r = 55 mph