SOLUTION: Hi! I have a problem that my professor wants me to solve by completing the square. The problem says: A train travels 300 miles at a uniform speed. If its speed had been 15 mile

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Hi! I have a problem that my professor wants me to solve by completing the square. The problem says: A train travels 300 miles at a uniform speed. If its speed had been 15 mile      Log On


   

Question 1128578: Hi! I have a problem that my professor wants me to solve by completing the square. The problem says:
A train travels 300 miles at a uniform speed. If its speed had been 15 miles per hour less, the trip would have taken 1 hour and 40 minutes more. Find the actual speed of the train.
I tried setting it up like this: (x/300)-([x-15]/300)=1.667
Thank you!
Found 3 solutions by ikleyn, greenestamps, josgarithmetic:
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.

I am just in a serious jam.


From one side, you said "the professor wants YOU to solve the problem".


But if I will solve it for you, it will be NOT what the professor wants to get from you.



/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/

Madelynn, I got your message - thank you for your explanations - I fully understand it !


Next time start your post simpler: 

       Please explain me how to setup this problem  . . . 

    or

       Please teach me how to solve this problem . . . "

and all the tutors will be happy to help you.


By the way, you will find many similar Travel & Distance problems solved and carefully explained in the lessons
    - Selected Travel and Distance problems from the archive
    - Had a car move faster it would arrive sooner
in this site.

There are also other similar problems from other areas, solved and explained in the lessons
    - Had they sold . . .
    - Challenging word problems solved using quadratic equations
in this site.


                    H a p p y   l e a r n i n g  ! !


------------

In one book I read very wise thought: 

      - What is a happiness ?


    and the answer:


       - The happiness is to hear singing of a girl after she learned a way from you . . .


Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


(1) Don't use a decimal approximation for the number of hours. Use 5/3 hours.

(2) Time is distance divided by speed -- not speed divided by distance.

(3) The greater time is at the lower speed; the the 5/3 hours difference is (time at lower speed) minus (time at higher speed). You have the two expressions in the wrong order in your equation.

So....

300%2F%28x-15%29+-+300%2Fx+=+5%2F3

Multiply everything by the common denominator, x(x-15); and multiply everything by 3/5 to get rid of the fraction on the right.

That will give you the quadratic equation which you can solve by completing the square.

Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!

300%2F%28r-15%29-300%2Fr=1%262%2F3,5%2F3
-
3r%28r-15%29%28300%2F%28r-15%29-300%2Fr%29=3r%28r-15%29%285%2F3%29
.
.
180%2A15=r%5E2-15r

r%5E2-15r=2700------------from here, if your instructions are to use Completing the Square, the term to use is %2815%2F2%29%5E2, to add to both sides.
.
.


( answer: r=60 )