Marathon runner velocity problem

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To qualify for a marathon of 42.195 kilometers in 3 hours and 15 minutes, a runner must maintain an average velocity of 3.6 m/s. The calculation involves converting kilometers to meters and time from hours and minutes to seconds. The initial confusion arose from incorrect unit cancellation during the conversion process. After clarifying the calculations, the correct average speed was confirmed as 3.6 m/s. Understanding unit conversions is crucial for accurate velocity calculations in running.
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1. Consider a marathon of 42.195 kilometers. In order to attain the qualifying time of 3 hours and 15 minutes to enter the race, a runner would need to run at an average velocity (in m/s) of



2. I thought this would be average speed = distance traveled/time interval spent traveling



3. Since they wanted it in terms of m/s, I divided 42.195 by 1000. Then to get seconds, I converted 3 hr and 15 mins to 11700 seconds, which gives 3.6E-6.

But apparently its wrong. Help?
 
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Why did you divide by 1000?
 


To go from kilometers to meters
 


You are not canceling units correctly:

1 km * 1000 \frac{m}{km} = 1000 m
 


Ohhh, the right is answer is 3.6 then. Thanks! That makes more sense.
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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