Question 472643
brenda walks at 4 km/h.
brenda jogs at 8 km/h.
the loop is 6 km long.
on tuesday, the total time it took to do the loop = 1 hour.
j = amount of hours she spent jogging.
w = amount of hours she spent walking.
first equation is:
j + w = 1
let d1 = the distance she went walking.
let d2 = the distance she went jogging.
second equation is:
d1 + d2 = 6
the formula to use to solve this type of problem is:
rate * time = distance
for walking, we get:
4 * w = d1
for jogging, we get:
8 * j = d2
since we know that d1 + d2 = 6, then we add these equations together to get:
4*w + 8*j = 6
since we know that j + w = 1, we can solve for either one and use that to solve the equation for one of the variables.
we'll use j = 1 - w.
the equation of 4*w + 8*j = 6 becomes:
4*w + 8*(1-w) = 6
expand this to get:
4*w + 8 - 8*w = 6
subtract 8 from both sides of this equation to get:
4*w - 8*w = -2
combine like terms to get:"
-4*w = -2
divide both sides of this equation by -4 to get:
w = 2/4 = 1/2
this means that j also equals 1/2 because j + w = 1
this means that brenda walked for 1/2 hour and jogged for 1/2 hour.
if she walked for 1/2 hour at 4 km/h then she walked for 2 km.
if she jogged for 1/2 hour at 8 km/h then she jogged for 4 km.
2 km + 4km = 6 km which is the distance of the loop.
numbers check out.
answers to your questions are:
a.	Set up a system of equations to model this situation. How did you figure out what each equation would be? Let j = time spent jogging and w = time spent walking.
see the work above.
the system of equations that was used to solve the problem was:
d1 + d2 = 6
j + w = 1
4*w = d1
8*j = d2
d1 was the walking distance in km.
d2 was the jogging distance in km.
w was the walking time in hours.
j was the jogging time hours.
4 was the walking rate of speed in km/h.
8 was the jogging rate of speed in km/h.
b.	Solve this system of equations, showing all your work.
done. 
c.	How much time did Brenda spend jogging on Tuesday?
1/2 hour.
d.	How much time did Brenda spend walking on Tuesday?
1/2 hour.
e.	How far, in km, did Brenda jog on Tuesday?
4 km.
f.	How far, in km, did Brenda walk on Tuesday?
2 km.