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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)= 6.25--correct.
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.