SOLUTION: A person jogs 3.5 miles and walks and additional 4 miles. He jogs 4.5 mph faster than he walks. The total exercise time is 6 hrs. Find the speeds.

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Question 434776: A person jogs 3.5 miles and walks and additional 4 miles. He jogs 4.5 mph faster than he walks. The total exercise time is 6 hrs. Find the speeds.
Answer by jorel1380(3719) About Me  (Show Source):
You can put this solution on YOUR website!
Let x be the person's walking speed.
------------------------------
4/x+3.5/(x+4.5)=6
Multiply each side by (x)(x+4.5)
4(x+4.5)+3.5(x)=6(x2+4.5x)
4x+18+3.5x=6x2+27x
8x+36+7x=12x2+54x
0=12x2+39x-36
0=(4x-3)(3x+12)
x=3/4,-4
His walking speed is .75 mph, jogging is 5.25
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 12x%5E2%2B39x%2B-36+=+0) has the following solutons:

x%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=%2839%29%5E2-4%2A12%2A-36=3249.

Discriminant d=3249 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-39%2B-sqrt%28+3249+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2839%29%2Bsqrt%28+3249+%29%29%2F2%5C12+=+0.75
x%5B2%5D+=+%28-%2839%29-sqrt%28+3249+%29%29%2F2%5C12+=+-4

Quadratic expression 12x%5E2%2B39x%2B-36 can be factored:
12x%5E2%2B39x%2B-36+=+12%28x-0.75%29%2A%28x--4%29
Again, the answer is: 0.75, -4. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+12%2Ax%5E2%2B39%2Ax%2B-36+%29