Boats and Streams – Infer stream speed from unequal travel times: A motorboat has still-water speed 30 km/h. It travels from Mumbai to Goa in 2 hours, then later from Goa back to Mumbai in 4 hours. Assuming the stream speed is constant in both trips, what is the speed of the stream?

Introduction / Context:
Different times for the same route in opposite directions reflect downstream and upstream effects. With known still-water speed u and unknown current v, the distance D is equal on both legs, allowing a simple equation in v.

Given Data / Assumptions:

• Still-water speed u = 30 km/h.
• Downstream time = 2 h; upstream time = 4 h.
• Distance Mumbai–Goa is the same both ways.

Concept / Approach:
Let D be the common distance. Then D = (u + v)*2 and D = (u − v)*4. Equate and solve for v.

Step-by-Step Solution:
2(30 + v) = 4(30 − v).60 + 2v = 120 − 4v ⇒ 6v = 60 ⇒ v = 10 km/h.

Verification / Alternative check:
Using v = 10, downstream speed 40 km/h for 2 h gives D = 80 km; upstream speed 20 km/h for 4 h also gives 80 km.

Why Other Options Are Wrong:
Any value not equal to 10 km/h breaks the equality of distances for the two legs.

Common Pitfalls:
Assuming different distances or averaging speeds arithmetically without considering direction and current.

Final Answer:
10 km/h