A boat takes 3 hours to go 36 km upstream and 2 hours to return downstream. What

A boat takes 3 hours to go 36 km upstream and 2 hours to return downstream. What is the speed of the stream?

A boat takes 3 hours to go 36 km upstream and 2 hours to return downstream. What is the speed of the stream?

Correct Answer: 2 km/h

Step 1: Understand that the boat travels upstream and downstream. Upstream is against the current, and downstream is with the current.
Step 2: Let the speed of the boat in still water be 'y' km/h and the speed of the stream be 'x' km/h.
Step 3: When the boat goes upstream, its effective speed is (y - x) km/h. When it goes downstream, its effective speed is (y + x) km/h.
Step 4: The boat takes 3 hours to go 36 km upstream. Use the formula: time = distance / speed. So, 3 = 36 / (y - x).
Step 5: Rearranging the equation gives us: y - x = 36 / 3, which simplifies to y - x = 12. (Equation 1)
Step 6: The boat takes 2 hours to return 36 km downstream. Again, use the formula: 2 = 36 / (y + x).
Step 7: Rearranging this equation gives us: y + x = 36 / 2, which simplifies to y + x = 18. (Equation 2)
Step 8: Now we have two equations: Equation 1 (y - x = 12) and Equation 2 (y + x = 18).
Step 9: Add both equations together: (y - x) + (y + x) = 12 + 18, which simplifies to 2y = 30.
Step 10: Solve for y: y = 30 / 2, which gives y = 15 km/h.
Step 11: Substitute y back into Equation 1: 15 - x = 12, which simplifies to x = 15 - 12.
Step 12: Therefore, x = 3 km/h, which is the speed of the stream.

Relative Speed – Understanding how the speed of a boat is affected by the speed of the stream when moving upstream and downstream.
Distance, Speed, Time Relationship – Applying the formula distance = speed × time to solve for unknowns in motion problems.
Algebraic Manipulation – Using algebra to set up and solve equations based on the given information.