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

## Homework Statement

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?

## Homework Equations

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

## 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.

#### Attachments

• simonhospital.png
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Mark44
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## Homework Statement

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?

## Homework Equations

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