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

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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)   (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)   (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....



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)   (Show Source): You can put this solution on YOUR website!

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------------from here, if your instructions are to use Completing the Square, the term to use is , to add to both sides.
.
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( answer: r=60 )
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