# Simon suffers an injury at a campsite on the bank of a canal

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1. Dec 19, 2014

### ilii

1. The problem statement, all variables and given/known data
Simon suffers an injury at a campsite on the bank of a canal that is 6sqrt(2) km wide. if he is able to paddle his kayak at 5km/h and pedal a bicycle at 15km/h along the opposite bank, where should be land on the opposite bank to reach the hospital in minimum time?

2. Relevant equations
assuming Pythagorean theorem , etc.
when you find the equation, then find the derivative and make it = 0 to find max/min

3. The attempt at a solution
I get the hypotenuse to c=6sqrt(2)+x but don't know where to go from here. Help would be appreciated. Diagram included and is an exact copy of the diagram that was provided with the question.

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• ###### simonhospital.png
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2. Dec 19, 2014

### Staff: Mentor

What makes you think that is the hypotenuse? What you have is just the sum of the width of the canal and the distance down the other side. In your relevant equations, you list the theorem of Pythagoras. Do you know how to use it to find the hypotenuse of a right triangle?

3. Dec 19, 2014

### Joffan

Simon paddles the hypoteneuse at 5km/h, taking time $t_p$, then cycles the remaining distance at 15km/h, taking time $t_c$. Total time $t = t_p+t_c$, which will be a function of x.

Last edited: Dec 19, 2014