A man launches his boat from point A on a bank of a straight river, 4 km wide, a
ID: 2831911 • Letter: A
Question
A man launches his boat from point A on a bank of a straight river, 4 km wide, and wants to reach point B, 3 km downstream on the opposite bank, as quickly as possible (see the figure below). He could row his boat directly across the river to point C and then run to B, or he could row directly to B, or he could row to some point D between C and B and then run to B. If he can row 6 km/h and run 8 km/h, where should he land to reach B as soon as possible? (We assume that the speed of the water is negligible compared to the speed at which the man rows.) Give your answer in km from C.
Explanation / Answer
let CD = x
=>
total time f(x)= [(16+x^2)^0.5]/6 + (3-x)/8
=>
f'(x) = x/6[(16+x^2)^0.5] -1/8 <0 for x<3
=>
f is decrasing for x<3
=>
He should at B( 3 KM from C)
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