A boat travels along a river at 15 km/h relative to the water and the current speed is 3 km/h. Find the speed of the boat relative to the bank downstream and upstream — Physics problems | PhysLabo
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Speed of a boat downstream and upstream

Easy 9 grade Mechanics / Motion

A boat travels along a river at a speed of $v_{\text{boat}} = 15$ km/h relative to the water. The speed of the current is $v_{\text{cur}} = 3$ km/h. Find the speed of the boat relative to the bank downstream and upstream.

Given
  • $v_{\text{boat}} = 15$ km/h
  • $v_{\text{cur}} = 3$ km/h
  • $v_{\text{down}} = ?,\ v_{\text{up}} = ?$
Visual demonstration
Hints
Hint 1 / 2
The speed of the boat is given relative to the water, while the current is the speed of the water relative to the bank: these speeds add up.
Hint 2 / 2
Downstream the speeds point in the same direction (add), upstream in opposite directions (subtract).
Solution

Velocities along the same direction add up. Downstream:

$$v_{\text{down}} = v_{\text{boat}} + v_{\text{cur}} = 15 + 3 = 18 \text{ km/h}$$

Upstream:

$$v_{\text{up}} = v_{\text{boat}} - v_{\text{cur}} = 15 - 3 = 12 \text{ km/h}$$

Answer

Downstream $18$ km/h, upstream $12$ km/h