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.
Jordan, if you are in ALG II, I recommend a tutor before you get lost.
To solve this problem, let's define two variables:
Let w represent the walking rate (in miles per hour)
Let j represent the jogging rate (in miles per hour)
Now, let's set up a system of equations using the given information:
Equation 1: 2w + 0.5j = 6.25 (from Lucy's activity yesterday)
Equation 2: 3w + 1j = 10.25 (from Lucy's activity today)
To solve this system, you can use the method of substitution or elimination.
We'll use the method of elimination. Multiply both sides of Equation 1 by 3 to make the coefficients of j in both equations the same:
3 * (2w + 0.5j) = 3 * 6.25
6w + 1.5j = 18.75
Now, we'll multiply both sides of Equation 2 by 2 to make the coefficients of j in both equations the same:
2 * (3w + 1j) = 2 * 10.25
6w + 2j = 20.50
Now, subtract Equation 2 from Equation 1 to eliminate the j term:
(6w + 1.5j) - (6w + 2j) = 18.75 - 20.50
6w + 1.5j - 6w - 2j = -1.75
Simplifying this equation, we get:
-0.5j = -1.75
Now, solve for j:
j = -1.75 / -0.5
j = 3.5
So, the jogging rate is 3.5 miles per hour.
Now, substitute this value of j into either Equation 1 or Equation 2 to solve for w. Let's use Equation 1:
2w + 0.5(3.5) = 6.25
2w + 1.75 = 6.25
2w = 6.25 - 1.75
2w = 4.5
w = 4.5 / 2
w = 2.25
So, the walking rate is 2.25 miles per hour.
To verify our solution, we can check whether the values of w and j satisfy the second equation:
3(2.25) + 1(3.5) = 6.75 + 3.5 = 10.25
Therefore, the solution is correct.
Lucy's walking rate is 2.25 miles per hour and her jogging rate is 3.5 miles per hour.