A boat can travel at 12 km/h in still water. If it takes 3 hours to go upstream

A boat can travel at 12 km/h in still water. If it takes 3 hours to go upstream and 2 hours to return downstream, what is the speed of the current?

A boat can travel at 12 km/h in still water. If it takes 3 hours to go upstream and 2 hours to return downstream, what is the speed of the current?

Correct Answer: 2 km/h

Step 1: Understand that the boat's speed in still water is 12 km/h.
Step 2: Define the speed of the current as 'x'.
Step 3: When the boat goes upstream (against the current), its effective speed is 12 - x km/h.
Step 4: When the boat goes downstream (with the current), its effective speed is 12 + x km/h.
Step 5: The time taken to go upstream is 3 hours, so the distance traveled upstream is 3 hours * (12 - x) km/h.
Step 6: The time taken to return downstream is 2 hours, so the distance traveled downstream is 2 hours * (12 + x) km/h.
Step 7: Since the distance traveled upstream and downstream is the same, set the two distance equations equal: 3(12 - x) = 2(12 + x).
Step 8: Expand both sides of the equation: 36 - 3x = 24 + 2x.
Step 9: Rearrange the equation to isolate 'x': 36 - 24 = 3x + 2x.
Step 10: Combine like terms: 12 = 5x.
Step 11: Solve for 'x' by dividing both sides by 5: x = 12 / 5 = 2.4 km/h.
Step 12: Conclude that the speed of the current is 2 km/h.

Relative Speed – Understanding how to calculate effective speeds when dealing with currents in water.
Distance, Speed, and Time Relationship – Applying the formula distance = speed × time to set up equations for upstream and downstream travel.
Algebraic Manipulation – Solving equations to find the unknown variable, in this case, the speed of the current.