The speed of the current is 4kph. A boat travels 6km upstream in the same time it takes to travel 10km downstream. What is the spees of the boat in still water?
distance=(current+boat)*time
Upstream:
6km=(B-4)t
Downstream
10km=(b+4)t
the times are identical, so
6/(B-4)=10/(B+4) or
6(B+4)=10(B-4)
solve for B..
4B=16
B=4km/hr
To solve this problem, we need to use the concept of relative speed.
Let's assume the speed of the boat in still water is 'b' km/h. The speed of the current is given as 4 km/h.
When the boat travels upstream, its effective speed is reduced by the speed of the current. So, the effective speed upstream would be (b - 4) km/h.
When the boat travels downstream, its effective speed is boosted by the speed of the current. So, the effective speed downstream would be (b + 4) km/h.
Now, we can set up a ratio based on the given information:
Upstream Distance / Speed Upstream = Downstream Distance / Speed Downstream
6 km / (b - 4) km/h = 10 km / (b + 4) km/h
To solve this equation, we can cross-multiply:
6(b + 4) = 10(b - 4)
6b + 24 = 10b - 40
Rearranging the equation:
10b - 6b = 24 + 40
4b = 64
Dividing both sides by 4:
b = 16
Therefore, the speed of the boat in still water is 16 km/h.