Answer:
12 km/h
Step-by-step explanation:
Given: Distance covered by boat downstream = 50 km
Distance covered by boat upstream = 30 km
Time taken by boat in down stream and upstream are equal.
Speed of the stream = 3 km/h
Let x be the speed of boat in still water.
∴ Speed of boat in downstream [tex](s_1)[/tex] = [tex](x+3)\ km/h[/tex]
Speed of boat in upstream [tex](s_2)[/tex] = [tex](x-3)\ km/h[/tex]
As we know, [tex]Time = \frac{Distance}{speed}[/tex]
And time remain same for both upstream and downstream
∴ [tex]\frac{50}{(x+3)} = \frac{30}{(x-3)}[/tex]
Now, cross multiply both side
⇒ [tex]50\times (x-3) = 30\times (x+3)[/tex]
⇒ [tex]50x-30x = 150+90[/tex]
∴ [tex]x= 12\ km/h[/tex]
∴ Speed of boat in still water is 12 km/h
