Max/min question (1 Viewer)

[enigma_1]

How do you get the equation for this? And then can you please derive it? im not getting it

a man in a boat B, 25m from the nearest point A, on a straight shore, wants to reach a point C, ,50 m from A along the shore, in the least time. he can row at 4m/s and walk 6m/s. Where should he land?

Thanks

 

[cineti970128]

With max/min question Always draw a diagram.
Let X be a random point on AC and let x be the distance AX
Then 0<x<30 including 0 and 30
Then distance BX travelled is using Pythagoras, = (625+x^2)^ 1/2
Hence the time(BX) = {(625+x^2)^ 1/2} ÷ 4

The distance XC travelled is simply 50-x
Hence the time = (50-x) ÷6


You add these two functions and differentiate it.
For x= 25/(35)^ 1/2
= 4.22
Time minimum using the table of values
Therefore he should land 4.22m right of A