SOLUTION: Question: By increasing her usual speed by 25 kilometers per hour, a bus driver decreases the time on a 25 kilometer trip by 10 minutes. Find the usual speed. If I set up the pr

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Question: By increasing her usual speed by 25 kilometers per hour, a bus driver decreases the time on a 25 kilometer trip by 10 minutes. Find the usual speed. If I set up the pr      Log On


   

Question 153988: Question: By increasing her usual speed by 25 kilometers per hour, a bus driver decreases the time on a 25 kilometer trip by 10 minutes. Find the usual speed.
If I set up the problem as:
25/x+25 = 25/x - 1/6
I get two seperate answers and it all depends on how I do the LCD.
the LCD which is 6x(x+25) and multiply that out I get
25(6x) = 6(x+25)(25) + x(x+25)
150x = 6x + 150 + 150 - x^2 - 25x combine like terms and I get
x^2 + 169x - 300 = 0
I can't seem to factor that one out.
the second problem:
25(6x) = 25(x+25)(6) - x(x+25)(x)
150x = 25x + 625 + 150 - x - 125 -x
150x = 23x + 650 + x^2
x^2 + 127x -650 = 0
What I am asking help on is if I even have a general idea of what to do. I am stuck at factoring them both out and unfortunatly this question is an even number so there is no solution in the manual or answer in the back of the book.
Thanks for any help :)
Answer by orca(409) About Me  (Show Source):
You can put this solution on YOUR website!
There is only one error in your working. That happened when you expand
6%28x+%2B+25%29%2A25
Its expanded form is:
6%28x+%2B+25%29%2A25
=6%2A25%28x%2B25%29
=6%2A25x+%2B6%2A25%2A25 (multiply each terms in the parentheses by 6*25)
=150x%2B6%2A25%2A25
So
25%286x%29=6%2A%28x%2B25%29%2A25-x%28x%2B25%29
becomes:
150x=150x%2B6%2A25%2A25-x%5E2-25x
Combining like terms, we have:
x%5E2%2B25x-6%2A25%2A25=0
To factor the left side, note that -6*25*25 =3*25*(-2*25)=75*(-50).
As 75 + (-50) = 25, so x%5E2%2B25x-6%2A25%2A25=%28x%2B75%29%28x-50%29
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Also note that there is an typing error in the equation:
25(6x) = 6(x+25)(25) + x(x+25)
The sign before the term x(x+25) should be "-".