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

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) (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) (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
:
multiplied out right side
:
put 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 (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=580 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 7.0415945787923, -17.0415945787923. Here's your graph:

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