The total time taken to go from pier A to B and back is required.
The total time taken is [tex]4.167\ \text{hours}=4\ \text{hours}\ \text{and}\ 10\ \text{minutes}[/tex]
Time is given by
[tex]\text{Time}=\dfrac{\text{Distance}}{\text{Speed}}[/tex]
v = Speed of boat in still water = 25 km/h
s = Distance between pier A and B = 50 km
Speed of current is 5 km/h
At one time the boat will go along the current. So, speed will be added.
At another time the boat will go against the current. So, speed will be subtracted.
Total time will be
[tex]t=\dfrac{s}{v+5}+\dfrac{s}{v-5}\\\Rightarrow t=\dfrac{s(v-5)+s(v+5)}{v^2-25}\\\Rightarrow t=\dfrac{sv-5s+vs+5s}{v^2-25}\\\Rightarrow t=\dfrac{2vs}{v^2-25}\\\Rightarrow t=\dfrac{2\times 25\times 50}{25^2-25}\\\Rightarrow t=\dfrac{25}{6}\ \text{hours}=\dfrac{25}{6}\times 60=250\ \text{minutes}\\\Rightarrow t=4\ \text{hours}\ \text{and}\ 10\ \text{minutes}[/tex]
The total time taken is [tex]4.167\ \text{hours}=4\ \text{hours}\ \text{and}\ 10\ \text{minutes}[/tex]
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