Trains, Boats, and Streams Formulas

1. Speed of Boat in Still Water Formula

$\mathrm{Speed\; of\; Boat\; in\; Still\; Water}=\frac{\mathrm{Speed\; of\; Boat\; in\; Stream}+\mathrm{Speed\; of\; Stream}}{2}$

Average speed of the boat downstream and the stream.

2. Speed of Boat in Stream Formula

$\mathrm{Speed\; of\; Boat\; in\; Stream}=\frac{\mathrm{Speed\; of\; Boat\; in\; Still\; Water}+\mathrm{Speed\; of\; Stream}}{2}$

Average of the boat’s still water speed and the stream speed.

3. Relative Speed Formula (Trains)

$\mathrm{Relative\; Speed}=\mathrm{Speed\; of\; Train\; 1}+\mathrm{Speed\; of\; Train\; 2}$

Sum of speeds for opposite directions, or difference for same direction.

4. Time to Cross Each Other Formula (Trains)

$\mathrm{Time\; to\; Cross\; Each\; Other}=\frac{\mathrm{Sum\; of\; Lengths\; of\; Both\; Trains}}{\mathrm{Relative\; Speed}}$

Time = total length divided by relative speed.

5. Time to Cross a Pole Formula (Train)

$\mathrm{Time\; to\; Cross\; a\; Pole}=\frac{\mathrm{Length\; of\; the\; Train}}{\mathrm{Speed\; of\; Train}}$

Time = train length divided by its speed.

6. Time to Reach a Destination Formula (Boat)

$\mathrm{Time}=\frac{\mathrm{Distance\; to\; Destination}}{\mathrm{Speed\; of\; Boat}}$

Time = distance divided by speed.

7. Boat Moving Upstream Formula

$\mathrm{Speed\; of\; Boat\; Upstream}=\mathrm{Speed\; of\; Boat\; in\; Still\; Water}-\mathrm{Speed\; of\; Stream}$

Boat speed reduced by stream speed.

8. Speed of Stream Formula

$\mathrm{Speed\; of\; Stream}=\frac{\mathrm{Speed\; of\; Boat\; in\; Stream}-\mathrm{Speed\; of\; Boat\; in\; Still\; Water}}{2}$

Stream speed is half the difference between stream and still water speeds.

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