11th grade
posted by jordan .
Yesterday Lucy walked 2 hours and 1/2 jogged hour and covered 6.25 miles. Today she walked for 3 hours and jogged for 1 hour and covered 10.25 miles. Assuming a constant walking rate and a constant jogging rate, how fast did she walk and how fast did she jog? Define two variables, write a system of equations, and solve to find the walking rate and the jogging rate. Justify your answer by showing how you solved the problem.
w walking j jogging
2w + .5j= 6.25 > 3(2w+.5j)= 3(6.25)
3w + 1j= 10.25 > 2(3w+1j)= 2(10.25
6w + 1.5j= 18.75
6w  2j= 20.50

.5j=1.75
j=.3
2w + .5(.3)= 6.25
2w + 15= 6.25
2w= 6.10 w= 3.05
check:
2(3.05) + .5(.3)= 6.25 (correct)
3(3.05) + 1(.3)= 9.45(wrong!!) it should be 10.25.

since when is 1.75/5 = .3?

.5/1.75= .2857...or .3

Lord, Jordan.
you have a*x=b
then x= b/a NOT a/b 
I get 1.75/.5=3.5
check that. 
wow haha im lost...
6w + 1.5j= 18.75
6w  2j= 20.50

.5j=1.75
j=.3
? why would i multiply? 
Jordan, this is pretty basic.
.5 j= 1.75
divide both sides by .5
j= 1.75/.5 
But, if i did get 3.5 that would mess up getting 6.25 or 10.25.
2(3.05) + .5(.3)= 6.25correct.
3(3.05) + 1(.3)= 9.45... this is the one where i went wrong. i went wrong. 
You have a lot of problems. YOu solved j as 3.5 so now solve for w, you first answer is WRONG.
2w + .5(3.5)= 6.25 solve for w. 
Jordan, if you are in ALG II, I recommend a tutor before you get lost.