SOLUTION: Just like my other question, I keep coming with wrong equations, these are my final assignment and I have to get it right...I need help in word problems, my weakest part is comming

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: Just like my other question, I keep coming with wrong equations, these are my final assignment and I have to get it right...I need help in word problems, my weakest part is comming      Log On


   

Question 179311This question is from textbook
: Just like my other question, I keep coming with wrong equations, these are my final assignment and I have to get it right...I need help in word problems, my weakest part is comming up with the right equation...
Kim starts to walk 3 mi to school at
7:30 A.M. with a temperature of 0°F. Her brother Bryan
starts at 7:45 A.M. on his bicycle, traveling 10 mph faster
than Kim. If they get to school at the same time, then how
fast is each one traveling? This question is from textbook

Found 2 solutions by stanbon, Mathtut:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Kim starts to walk 3 mi to school at
7:30 A.M. with a temperature of 0°F.
Her brother Bryan starts at 7:45 A.M. on his bicycle,
traveling 10 mph faster than Kim.
If they get to school at the same time, then how
fast is each one traveling?
---------------------------
Kim DATA:
distance = 3 miles ; rate = x mph ; time = d/r = 3/x hrs
---------------------------------
Bryan DATA:
distance = 3 miles ; rate = x+10 mph ; time = d/r = 3/(x+10) hrs
---------------------------------
Equation:
Kim time - Bryan time = (1/4) hr
3/x - 3/(x+10) = 1/4
Divide thru by 3 to get:
1/x - 1/(x+10) = 1/12
Simplify:
12(x+10) - 12(x) = x(x+10)
12*10 = x^2 + 10x
x^2 + 10x - 120 = 0
x = [-10 +- sqrt(100 - 4*-120]/2
x = [-10 +- sqrt(580)]/2
Positive solution:
x = [-10 + 24.083]/2
x = 14.083/2
x = 7.0415 mph (Kim's rate)
x+10 = 17.0415 mph (Bryan's rate)
======================================
Cheers,
Stan H.

Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
we know the distance are equal 3 miles
:
lets call kims rate r and her time t
:
Bryan's r would be r+10 and his time would be t+1/4(remember this is all in hours)
:
Kim:::: 3=rt................eq 1
Bryan:: 3=(r+10)(t-(1/4))...eq 2
:
lets rewrite eq 1 to t=3/r and plug it into eq 2
:
3=(r+10)((3/r)-(1/4))
:
3=(r+10)((12-r)/4r)found common denominator 2nd term on the right
:
12r=(r+10)(12-r)....multiplied both sides by 4r
:
12r=12r-r%5E2%2B120-10rmultiplied out right side
:
r%5E2%2B10r-120=0put all terms on one side
:
r=7.04mph-Kim's rate, (as the negative value is thrown out)
:
r+10=17.04mph-Bryans rate
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ar%5E2%2Bbr%2Bc=0 (in our case 1r%5E2%2B10r%2B-120+=+0) has the following solutons:

r%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%2810%29%5E2-4%2A1%2A-120=580.

Discriminant d=580 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-10%2B-sqrt%28+580+%29%29%2F2%5Ca.

r%5B1%5D+=+%28-%2810%29%2Bsqrt%28+580+%29%29%2F2%5C1+=+7.0415945787923
r%5B2%5D+=+%28-%2810%29-sqrt%28+580+%29%29%2F2%5C1+=+-17.0415945787923

Quadratic expression 1r%5E2%2B10r%2B-120 can be factored:
1r%5E2%2B10r%2B-120+=+1%28r-7.0415945787923%29%2A%28r--17.0415945787923%29
Again, the answer is: 7.0415945787923, -17.0415945787923. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B10%2Ax%2B-120+%29