SOLUTION: ​Imogene's car traveled 660 mi averaging a certain speed. If the car had gone 6 mph​ faster, the trip would have taken 1 hour less. Find the average speed.

Algebra ->  Human-and-algebraic-language -> SOLUTION: ​Imogene's car traveled 660 mi averaging a certain speed. If the car had gone 6 mph​ faster, the trip would have taken 1 hour less. Find the average speed.      Log On


   

Question 1145951: ​Imogene's car traveled 660 mi averaging a certain speed. If the car had gone 6 mph​ faster, the trip would have taken 1 hour less. Find the average speed.
Answer by ikleyn(52776) About Me  (Show Source):
You can put this solution on YOUR website!
.
Let x be the average speed under the question.


Then the travel time for 660 miles distance is  660%2Fx hours.


The hypothetical travel time is  600%2F%28x%2B6%29  hours.


The difference is 1 hour :


    660%2Fx - 660%2F%28x%2B6%29 = 1  hour.


It is your basic equation, the "time" equation.


To solve it, multiply both sides by x*(x+6).  You will get


    660*(x+6) - 660x = x*(x+6).


Simplify and solve for x


    660*6 = x^2 + 6x

    x^2 + 6x - 3960 = 0

    x%5B1%2C2%5D = %28-6+%2B-+sqrt%286%5E2+%2B+4%2A3960%29%29%2F2 = %28-6+%2B-+125.861%29%2F2.


Only positive root makes sense  x = %28-6+%2B+126%29%2F2 = 60.


ANSWER.  The average speed under the question is 60 miles per hour.


CHECK.  660%2F60+-+660%2F%2860%2B6%29 = 11 - 10 = 1 hour.  ! Precisely correct

Solved.