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C3 Differentiation help please :)

Some students on an expedition reach the corner of a very muddy field. They need to reach the opposite corner as quickly as possible. They estimate they can walk along the edge of the field at the rate of 5km/h, and then cut across the field at 3km/h. The field is a square of 0.5km.

How far do they need to walk along the field before cutting across?
--

How would you go about solving this? I'm struggling a little bit with the wording of it. I know I will have to use the chain rule and I have got a few ideas but it would really help me if someone could explain it to me.

Thank you
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ztibor
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Original post by tommydeaks
Some students on an expedition reach the corner of a very muddy field. They need to reach the opposite corner as quickly as possible. They estimate they can walk along the edge of the field at the rate of 5km/h, and then cut across the field at 3km/h. The field is a square of 0.5km.

How far do they need to walk along the field before cutting across?
--

How would you go about solving this? I'm struggling a little bit with the wording of it. I know I will have to use the chain rule and I have got a few ideas but it would really help me if someone could explain it to me.

Thank you


They need to walk x km along the field
Then the the way across the field will
(12−x)2+(12)2\displaystyle \sqrt{\left( \frac{1}{\sqrt{2}}-x\right) ^2+\left( \frac{1}{\sqrt{2}}\right)^2}
Write down the time as the function of x, and determine the minimum.
(edited 13 years ago)

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