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. 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.
Where am i going wrong?
ok up to
-.5j=-1.75
then
j = 3.5 (you had j= .3)
back in 3w + j = 10.25
3w + 3.5 = 10.25
w = 2.25
It appears that there is a mistake in the calculation. Let's re-evaluate the equations and solve them correctly.
The given system of equations is:
2w + 0.5j = 6.25 ...(1)
3w + 1j = 10.25 ...(2)
To eliminate the variable "j" in order to solve for "w," we can multiply equation (1) by 2 and equation (2) by -1:
4w + j = 12.50 ...(3)
-3w - j = -10.25 ...(4)
Now, add equations (3) and (4) to eliminate the variable "j":
4w + j + (-3w) + (-j) = 12.50 + (-10.25)
w = 2.25
Next, substitute the value of "w" back into equation (1) to solve for "j":
2(2.25) + 0.5j = 6.25
4.5 + 0.5j = 6.25
0.5j = 6.25 - 4.5
0.5j = 1.75
j = 1.75 / 0.5
j = 3.5
Therefore, the walking rate is 2.25 miles per hour and the jogging rate is 3.5 miles per hour.
Now, let's check if our solution is correct:
Yesterday:
2(2.25) + 0.5(3.5) = 6.25
4.5 + 1.75 = 6.25 (correct!)
Today:
3(2.25) + 1(3.5) = 10.25
6.75 + 3.5 = 10.25 (correct!)
So, our solution satisfies both equations and is therefore correct.
I apologize for the previous error. The correct walking rate is 2.25 miles per hour and the jogging rate is 3.5 miles per hour.