Question

A motorboat, whose speed in 15 km/hr in still water goes 30 km downstream and comes back in a total of 4 hours 30 minutes. The speed of the stream (in km/hr) is:

Answer 1

Let the speed of the stream be $x$ $km/hr$

Speed downstream $=(15+x)km/hr$

Speed upstream $=(15-x)km/hr$

Distance travelled downstream$=30km$

Distance travelled upstream$=30km$

Time upstream$=\frac{\text{Distance upstream}}{\text{Speed upstream}}$

Time upstream$=\frac{30}{15-x}$

Time downstream$=\frac{\text{Distance downstream}}{\text{Speed downstream}}$

Time downstream$=\frac{30}{15-x}$

Total time taken $4.5hrs$

$4.5=\frac{30}{15-x}+\frac{30}{15+x}$

$4.5=\frac{30(15+x)+30(15-x)}{225-x^2}$

$4.5=\frac{900}{225-x^2}$

$225-x^2=200$

$x^2=25$

$x=5km/hr$

Hence the correct option is (B).