Im having difficulties solving for x in this problem:
a lighthouse is at point A, 4km offshore from the nearest point O of a straight beach; a store is at point B, 4km down the beach from O. if the lighthouse keeper can row 4km/hr & walk 5km/hr, how should he proceed in order to get from the lighthouse to the store in the least possible time?
Given: Distance from A to O : 4 km
Distance from O to B : 4 km
Constant Speed (to row) : 4 kmph
Constant Speed (to walk) : 5 kmph
Let C - a point between O and B
x - distance from O&C
(4-x) - distance from C&B
sqrt(16+x^2) - distance from A to C
Speed = Distance / Time hence T = Distance / Speed
Time = Time (row) + Time (walk)
= ( distance from A to C / Constant Speed to row ) + ( distance from C to B / Constant Speed to walk )
= ( sqrt(16+x^2) / 4 ) + ( (4-x)/5)
T' = ( x / 4sqrt(16+x^2) ) - ( 1/5 )
Equating T' = 0 results to x = 16 /3
since OB > OC where OB = 4 km and OC < 4
then x cannot be 16/3 because 16/3 > 4 !
HELP!!! im so confused!!!!