It took Todd 11 hours to travel over pack ice from one town in the Arctic to another town 330 miles away. During the return journey, it took him 15 hours. Assume the pack ice was drifting at a constant rate, and that Todd’s snowmobile was traveling at a constant speed relative to the pack ice. What was the speed of the snowmobile relative to the pack ice?

Question

It took Todd 11 hours to travel over pack ice from one town in the Arctic to another town 330 miles away. During the return journey, it took him 15 hours. Assume the pack ice was drifting at a constant rate, and that Todd’s snowmobile was traveling at a constant speed relative to the pack ice. What was the speed of the snowmobile relative to the pack ice?

Answer 1

To find the speed of the snowmobile relative to the pack ice, we can use the formula:

Distance = Speed × Time

Let's assume the speed of the snowmobile relative to the pack ice is represented by "S", and the distance between the two towns is 330 miles.

On the forward journey, Todd took 11 hours to travel the distance of 330 miles:
Distance = Speed × Time
330 miles = S × 11 hours
S = 330 miles / 11 hours
S = 30 miles per hour

On the return journey, Todd took 15 hours to travel the same distance:
330 miles = S × 15 hours
S = 330 miles / 15 hours
S = 22 miles per hour

Therefore, the speed of the snowmobile relative to the pack ice is 22 miles per hour.

Answer 2

To find the speed of the snowmobile relative to the pack ice, we need to calculate the average speed for each journey and then find the difference between them.

Average speed is calculated by dividing the total distance traveled by the total time taken.

For the first journey, Todd traveled 330 miles in 11 hours, so the average speed is:

Average speed (Journey 1) = Distance / Time = 330 miles / 11 hours = 30 miles per hour

For the return journey, Todd traveled the same distance of 330 miles but took 15 hours, so the average speed is:

Average speed (Journey 2) = Distance / Time = 330 miles / 15 hours = 22 miles per hour

Now, to find the speed of the snowmobile relative to the pack ice, we calculate the difference between the two average speeds:

Speed relative to pack ice = Average speed (Journey 1) - Average speed (Journey 2)
= 30 miles per hour - 22 miles per hour
= 8 miles per hour

Therefore, the speed of the snowmobile relative to the pack ice is 8 miles per hour.

Answer 3

s + p = 330/11 = 30

s - p = 330/15 = 22

adding eqns ... 2s = 52