Answer: 3.94 hours
Step-by-step explanation:
From the question, the following parameters are given:
Distance offshore = 4.5 miles
Distance downshore = 6 miles
Speed when running = 3.4 mph
Speed with boat = 1.8 mph
distance of boat rowing = sqrt(4.5^2 + x^2)
Where
Speed = distance/time
Time = distance/speed
Time = distance of boat rowing/1.8
distance of running = 6 - x
Time = (6-x)/3.4
total travel time
t = sqrt(4.5^2 + x^2)/1.8 + (6 - x)/3.4
dt/dx = x/(1.8×sqrt(4.5^2 + x^2) - 1/3.4
d^2t/dx^2 = +ve at any x
x is at its minimum when dt/dx=0
x/(1.8×sqrt(4.5^2 + x^2) = 1/3.4
x = 6/sqrt(253) × 4.5 = 1.697 miles
Substitute x in
t = sqrt(4.5^2 + x^2)/1.8 + (6 - x)/3.4
We obtaine
t = sqrt(4.5^2 + 1.697^2)/1.8 + (6 - 1.69)/3.4
t = 2.672+ 1.266 = 3.94 hours
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