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.

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) (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 (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=3249 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 0.75, -4. Here's your graph:

RELATED QUESTIONS
Zoha jogs 3 miles per hour faster than she walks. She jogs for 2 miles and then walks for (answered by orca)

Zoha jogs 3 miles per hour faster than she walks. She jogs for 2 miles and then walks for (answered by ankor@dixie-net.com)

Felipe jogs for 9 miles and then walks another 9 miles. He jogs 4.5 miles per hour... (answered by josmiceli)

Elliot jogs for 10 miles and then walks for another 10 miles. He jogs 2.5 miles per hour... (answered by stanbon)

Joe walks 4 miles and jogs 7 miles in a total of 2 hours. If his jogging speed is twice... (answered by ankor@dixie-net.com)

The distance between Village A and Village B is 5 miles. A person walks part of the way... (answered by solver91311)

Set up an equation and solve the following problem. Felipe jogs for 21 miles and then... (answered by ankor@dixie-net.com)

Felipe jogs for 10 miles and then walks another 10 miles. He jogs 1.5 miles per hour... (answered by ankor@dixie-net.com)

Felipe jogs for 12 miles and then walks another 12 miles. He jogs miles 2 per hour faster (answered by ankor@dixie-net.com)