A boat can travel at a speed of 8km/h in still water on a lake.In flowing water of a stream, it can move at 8km/h relative to the water in the stream.If the stream speed is 3km/h, how fast can the boat travel upstream and downstream?

Upstream? the difference in velocities, downstream the sum.

Does that make sense?

vbg=vbs+vsg
where vbg is velocity of boat relative to ground; vbs is veloicty of boat relative to stream, and vsg is velocity of stream relative to ground. But note, in the case of upstream, the velocity of the stream relative to ground is negative, so one is dealing with the difference of the velocities.

To determine the boat's speed upstream and downstream, we need to consider the velocities relative to the still water.

Let's assume the speed of the boat in still water is represented by V, and the speed of the stream is S.

1. Speed of the boat downstream:
When the boat is moving in the same direction as the stream, the effective velocity of the boat is the sum of the boat's velocity in still water (V) and the stream's velocity (S). So the speed downstream can be calculated as V + S.
In this case, V = 8 km/h and S = 3 km/h.
Therefore, the speed of the boat downstream is 8 km/h + 3 km/h = 11 km/h.

2. Speed of the boat upstream:
When the boat is moving in the opposite direction to the stream, the effective velocity of the boat is the difference between the boat's velocity in still water (V) and the stream's velocity (S). So the speed upstream can be calculated as V - S.
Again, V = 8 km/h and S = 3 km/h.
Therefore, the speed of the boat upstream is 8 km/h - 3 km/h = 5 km/h.

In summary:
- The boat can travel downstream at a speed of 11 km/h relative to the ground.
- The boat can travel upstream at a speed of 5 km/h relative to the ground.

To determine how fast the boat can travel upstream and downstream, we need to consider the speed of the boat relative to the ground.

Let's first consider the boat traveling upstream against the flow of the stream.

When the boat moves upstream, its speed relative to the ground will be reduced because it is moving against the current. So, to find the boat's speed upstream, we subtract the speed of the stream from the boat's speed in still water.

Therefore, the boat's speed upstream would be:
8 km/h (boat's speed in still water) - 3 km/h (stream speed) = 5 km/h

So, the boat can travel upstream at a speed of 5 km/h.

Now, let's consider the boat traveling downstream with the flow of the stream.

When the boat moves downstream, the speed of the stream adds to the boat's speed. So, to find the boat's speed downstream, we add the speed of the stream to the boat's speed in still water.

Therefore, the boat's speed downstream would be:
8 km/h (boat's speed in still water) + 3 km/h (stream speed) = 11 km/h

So, the boat can travel downstream at a speed of 11 km/h.

In summary, the boat can travel upstream at a speed of 5 km/h and downstream at a speed of 11 km/h.