Question

A motor boat whose speed is 15 km/hr in still water goes 30 km downstream and comes back in 4 hours 30 minutes. Determine the speed of the stream.

Answer 1

Let the speed of the stream be x km/hr. Then, 

Speed of boat downstream = (15 + x) km/hr 

and speed of boat upstream = (15 – x) km/hr

∴ \(\frac{30}{15+x}+\frac{30}{15-x}=4\frac12=\frac92\)

⇒ \(\frac{30(15-x)+30(15+x)}{(15+x)(15-x)}=\frac92\) ⇒ \(\frac{900}{225-x^2}=\frac92\) ⇒ 200 = 225 - x²

⇒ x² = 25 ⇒ x = 5 km/hr.