question_answer

A boat moves with a speed of \[5\text{ }km/h\]relative to water in a river flowing with a speed of \[3\text{ }km/h\]and having a width of\[1\text{ }km\]. The time taken around a round trip is

A)  \[5\text{ }min\]       

B)  \[60\text{ }min\]

C)  \[20\text{ }min\]      

D)  \[30\text{ }min\]

Correct Answer: D

Solution :

Time taken by the boat to reach the other side is \[~Time=\frac{~~distance}{~relative\text{ }speed}\] Relative speed \[=\sqrt{{{5}^{2}}-{{3}^{2}}}=\sqrt{16}=4km/h\] \[\therefore \] \[T=\frac{1\,\,km}{4\,\,km/h}=0.25h\] To come hack boat takes the same time, hence total time is \[T'=2\times 0.25=0.5h\] Also,         \[1\,h=60\min \] \[\therefore \] \[0.5\,h=30\,\min \]