Yesterday Lucy walked 2 hours and jogged 1/2 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.
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>> -.5j=-1.75
6w + 2j= -20.50 >> 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.
please tell me where im going wrong:)
I am lost here:
6w + 1.5j= 18.75>> -.5j=-1.75
6w + 2j= -20.50 >> j=.3
I think you should have
6w + 1.5j= 18.75>>
-6w - 2j= -20.50 >>
adding them,
.5j= 1.75
j= .35
and w= you do it.
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.
In your system of equations, you made a mistake in the equation 3w + 1j = 10.25. Instead of multiplying both sides by -2, it should be multiplied by -1 to correct the error. Here's the corrected system of equations:
2w + 0.5j = 6.25
3w + 1j = 10.25
To eliminate the decimal point, you can multiply both equations by 2:
4w + j = 12.5
6w + 2j = 20.5
Now, you can multiply the first equation by -2 and add it to the second equation to eliminate the "j" variable:
-8w - 2j = -25
6w + 2j = 20.5
------------------
-2w = -4.5
Divide both sides of the equation by -2:
w = 2.25
Now substitute the value of w into either of the original equations to find the value of j:
2(2.25) + 0.5j = 6.25
4.5 + 0.5j = 6.25
0.5j = 1.75
j = 1.75 / 0.5
j = 3.5
Therefore, Lucy walks at a speed of 2.25 miles per hour and jogs at a speed of 3.5 miles per hour.