A woman at a point A on the shore of a circular lake with radius 2 mi wants to arrive at the point C diametrically opposite A on the other side of the lake. She can bicycle at the rate of 5 mi/h and row a boat at 2.5 mi/h. What is the shortest amount of time she can travel to point C?

Question

aripotta · Answer

1.256 hrs

anonymous · Answer

OMG. How did you do that?

aripotta · Answer

circumference = pi times diameter 
c = 3.14(4)
c = 21.56

she only has to travel half of the circumference on her bike, so

21.56/2 = 6.28

she can travel at 5 mi/h on her bike

6.28 mi/5 mph = 1.256 hrs

and if she took the boat...

4 mi/2.5 mph = 1.6

aripotta · Answer

1.6 hrs*

aripotta · Answer

so the least amount of time is 1.256 hrs

aripotta · Answer

does that make sense?

anonymous · Answer

Yes it does, thank you! I didn't know it was two different equations.

aripotta · Answer

well yea, it has to be. there's two different distances and two different speeds :)

anonymous · Answer

I wasn't sure what to do with the radius 2. Since there was a graph. So the 3.14(4) helped a lot.

anonymous · Answer

Why wouldn't you use the circumference for the boat as well?

aripotta · Answer

because the boat is cutting through the circle, not going around it. it's going across the diameter. that's why we used 4

aripotta · Answer

4 mi/2.5 mph = 1.6 hrs
4 is the diameter. 2.5 mph is the speed of the boat

anonymous · Answer

OH! Okay. I understand now. Thank you! :)

aripotta · Answer

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aripotta · Answer

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