SOLUTION: 2. Brenda jogs and walks a loop that is 6 km long for exercise every day. Her walking speed, on average, is 4 km/hour, while her jogging speed is 8 km/hour. On Tuesday, the entire

Question 472643: 2. Brenda jogs and walks a loop that is 6 km long for exercise every day. Her walking speed, on average, is 4 km/hour, while her jogging speed is 8 km/hour. On Tuesday, the entire loop took her 1 hour. Set up one equation using the total amount of time. Set up the other equation using distance = rate x time (actually in this case it�s distance = rate walking x time walking + rate jogging x time jogging).
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.
b. Solve this system of equations, showing all your work.
c. How much time did Brenda spend jogging on Tuesday?
d. How much time did Brenda spend walking on Tuesday?
e. How far, in km, did Brenda jog on Tuesday?
f. How far, in km, did Brenda walk on Tuesday?

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
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.

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