Answer :
Answer:
The speed of the boat in still water is 12 km/hour.
Step-by-step explanation:
Given:
Boat goes 50 km downstream and 30 km upstream. The speed of the stream 3 km/hour.
Now, to find the speed of the boat in still water:
Let the speed of boat in still water be [tex]x km/hour[/tex].
The speed of the downstream be [tex]x+3[/tex]
And, the speed of the upstream be [tex]x-3[/tex]
And, now we find the time by putting the formula:
[tex]Time = \frac{Distance}{Rate}[/tex]
So, downstream time is:
[tex]downstream\ time = \frac{50}{x+3}[/tex]
So, upstream time is:
[tex]upstream\ time = \frac{30}{x-3}[/tex]
According to question:
Time upstream = Time downstream
[tex]\frac{30}{x-3} = \frac{50}{x+3}[/tex]
By cross multiplication:
[tex]30\times (x+3)= 50\times (x-3)[/tex]
[tex]30x+90=50x-150[/tex]
By taking variables in one side and taking numbers on the other side we get:
[tex]90+150=50x-30x[/tex]
[tex]240=20x[/tex]
Dividing both sides by 20 we get :
[tex]12=x[/tex]
Therefore, the speed of the boat in still water is 12 km/hour.