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It took Chuck 4 hours to travel over pack ice from one town in the Arctic to another town 200 miles away. During the return journey, it took him 10 hours. Assume the pack ice was drifting at a constant rate, and that Chuck’s snowmobile was traveling at a constant speed relative to the pack ice. What was the speed of Chuck's snowmobile?

Sagot :

facundo3141592

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.

How to find the system of equations:

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

Solving the system of equations:

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

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