A person in a boat on a lake is 9 km from the shore and must

A person in a boat on a lake is 9 km from the shore and must go to a store 12 km down the shoreline in the 1 shortest possible time The person can walk 8 km/hr and the boat can travel at 4 km/hr. Where from the store I should the person strike land for the shortest total travel time? Approximate to the nearest tenth.

Solution

distnace travelled by boat length of hypotenuse = sqrt(9^2 +d^2) = sqrt(81+d^2)

diatnec along the shore = 12 -d

Total time ,T= (sqrt(81+d^2)/4 + (12-d)/8

Minium time : find T\' = d/4sqrt(d^2 + 81) -1/8

Plug T\' =0 ;

d/4sqrt(d^2 + 81) -1/8 =0

On solving we get

we get d = 3sqrt3 .This would given minimume time

So, Person should strike shore 12 -d from the store = 12 -3sqrt3

= 6.8 km