A person rows at 5 km/h in still water. It takes thrice as much time to go 40 km upstream as 40 km downstream. Find the speed of the stream.
Speed of stream = 2.5 km/h.
Step 1: Let the speed of the stream be \(s\) km/h.
Step 2: When rowing upstream (against the current), the water slows the boat down. So, effective speed = (speed in still water – speed of stream) = \(5 - s\) km/h.
Step 3: When rowing downstream (with the current), the water helps the boat go faster. So, effective speed = (speed in still water + speed of stream) = \(5 + s\) km/h.
Step 4: Time is calculated as distance ÷ speed. - Time to go 40 km upstream = \(\dfrac{40}{5 - s}\). - Time to go 40 km downstream = \(\dfrac{40}{5 + s}\).
Step 5: It is given that upstream time is three times the downstream time. So, \(\dfrac{40}{5 - s} = 3 \times \dfrac{40}{5 + s}\).
Step 6: Cancel 40 from both sides: \(\dfrac{1}{5 - s} = \dfrac{3}{5 + s}\).
Step 7: Cross-multiply: \(5 + s = 3(5 - s)\).
Step 8: Simplify: \(5 + s = 15 - 3s\). Add \(3s\) on both sides → \(5 + 4s = 15\). Subtract 5 → \(4s = 10\). Divide by 4 → \(s = 2.5\).
Final Answer: The speed of the stream is 2.5 km/h.