Table of Contents
Boats and Streams
Boats and Streams Formulas
Definitions
Let:
- \( B \) be the speed of the boat in still water
- \( S \) be the speed of the stream
Speed Downstream
The speed of the boat when moving in the same direction as the stream:
\[
\text{Speed Downstream} = B + S
\]
Speed Upstream
The speed of the boat when moving against the direction of the stream:
\[
\text{Speed Upstream} = B - S
\]
Time Downstream
The time taken to cover a certain distance \( D \) downstream:
\[
\text{Time Downstream} = \frac{D}{B + S}
\]
Time Upstream
The time taken to cover a certain distance \( D \) upstream:
\[
\text{Time Upstream} = \frac{D}{B - S}
\]
Distance Covered Downstream
The distance covered downstream in time \( T \):
\[
\text{Distance Downstream} = T \times (B + S)
\]
Distance Covered Upstream
The distance covered upstream in time \( T \):
\[
\text{Distance Upstream} = T \times (B - S)
\]
Average Speed for Round Trip
If the boat goes a certain distance downstream and returns upstream:
\[
\text{Average Speed} = \frac{2 \times B \times S}{B + S}
\]