A) 2h
B) 2h 40 min
C) 1h 20 min
D) Cannot be estimated with the information given
Correct Answer: B
Solution :
Boat covers distance of 16km in a still water in 2 hours. i.e. \[{{v}_{B}}=\frac{16}{2}=8\,km/hr\] Now velocity of water \[\Rightarrow {{v}_{w}}=4km/hr\]. Time taken for going upstream \[{{t}_{1}}=\frac{8}{{{v}_{B}}-{{v}_{w}}}\]\[=\frac{8}{8-4}=2hr\] (As water current oppose the motion of boat) Time taken for going down stream \[{{t}_{2}}=\frac{8}{{{v}_{B}}+{{v}_{w}}}\]\[=\frac{8}{8+4}=\frac{8}{12}hr\] (As water current helps the motion of boat) \[\therefore \] Total time \[={{t}_{1}}+{{t}_{2}}=\left( 2+\frac{8}{12} \right)hr\] or 2hr 40min
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