A boat goes downstream a distance of X kilometres in two hours. It covers the…

Concept

When a boat travels in a stream, the stream changes its effective speed relative to the bank: going downstream the stream adds to the boat’s still-water speed, going upstream it subtracts.

• Downstream speed = still-water speed + stream speed

• Upstream speed = still-water speed − stream speed

• Subtracting the second from the first: Downstream speed − Upstream speed = 2 × stream speed

So the still-water speed cancels out, and the difference of the two journey speeds always equals twice the stream speed. Whenever the same distance is covered both ways, the two given times fix both speeds in terms of that distance, and this relationship then fixes the distance.

Application

1. Downstream leg: the boat covers X km in 2 hours, so downstream speed = X ÷ 2 = X/2 km/h.

2. Upstream leg: the same X km takes 3 hours, so upstream speed = X ÷ 3 = X/3 km/h.

3. Apply the relationship with a stream speed of 3 km/h: X/2 − X/3 = 2 × 3 = 6.

4. Take the LCM of 2 and 3, which is 6: 3X/6 − 2X/6 = 6, that is X/6 = 6.

5. Multiply both sides by 6: X = 36 km.

6. The question asks for 2X, not X: 2X = 2 × 36 = 72.

Cross-check

Substitute X = 36 km back into the original data and recompute the stream speed independently:

The recomputed stream speed of 3 km/h matches the value given in the question, so X = 36 km and the required value 2X = 72.