Final answer:
By using the concept of relative velocity, we can determine that the current's speed in the river is 6 km/h, which corresponds to option B.
Step-by-step explanation:
To determine how fast the current is, we need to understand the concept of relative velocity in the context of river problems. Akira's rowing speed in still water (his boat's speed), which we'll call boat speed (vb), combined with the speed of the river current (current speed (vc)), will give us his resulting speed downstream or upstream.
When Akira is rowing downstream, the current is helping him, so his effective speed is vb + vc. The distance covered downstream is 60 kilometers in 3 hours, so his effective speed downstream is 60 km / 3 h = 20 km/h.
When rowing upstream, against the current, his effective speed is vb - vc. The distance covered upstream is 32 kilometers in 4 hours, so his effective speed upstream is 32 km / 4 h = 8 km/h.
We can now set up two equations based on the downstream and upstream speeds:
- Downstream: vb + vc = 20 km/h
- Upstream: vb - vc = 8 km/h
Adding these two equations, we get:
2vb = 28 km/h
Thus, vb (boat speed in still water) = 28 km/h / 2 = 14 km/h.
We now subtract the two equations to solve for the current speed (vc):
(vb + vc) - (vb - vc) = 20 km/h - 8 km/h
2vc = 12 km/h
So, vc = 12 km/h / 2 = 6 km/h. The current's speed is therefore 6 km/h, which corresponds to option B.