We want to find the speed of Chuck's snowmobile, we will get that by solving a system of equations. We will find that the speed of Chuck's snowmobile is 35 mi/h.
1) First, we need to use the given information to find the equations:
We know that when Chuck travels in the same direction that the pack ice moves, the total velocity of Chuck is:
(S + R)
Where S is the speed of Chuck's snowmobile and R is the speed of the pack.
When he moves in the opposite direction in which the pack moves, the total velocity of Chuck is:
(S - R)
We know that first, it takes 4 hours to travel a distance of 200 miles, then we have:
(S + R)*4h = 200mi
Finally, it takes 10 hours to travel the same distance, then we have:
(S - R)*10h = 200mi
2) Now that we know the two equations, our system of equations is:
(S + R)*4h = 200mi
(S - R)*10h = 200mi
We want to solve this for the variable S, then we need to isolate R in one of the two equations, I will isolate R in the second one.
S - R = 200mi/10h = 20 mi/h
R = S - 20 mi/h
Now we can replace this into the other equation to get:
(S + R)*4h = 200mi
(S + S - 20mi/h)*4h = 200mi
Now we can solve this for S:
(2*S - 20 mi/h)*4h = 200mi
(2*S - 20 mi/h) = 200mi/4h = 50mi/h
2*S = 50mi/h + 20mi/h = 70 mi/h
S = (70mi/h)/2 = 35 mi/h.
This means that the speed of Chuck's snowmobile is 35 miles per hour.
If you want to learn more about systems of equations, you can read:
https://brainly.com/question/13729904
