A boat can travel at 18 km/h in still water. If it takes 4 hours to go upstream

A boat can travel at 18 km/h in still water. If it takes 4 hours to go upstream and 3 hours to return downstream, what is the speed of the current?

A boat can travel at 18 km/h in still water. If it takes 4 hours to go upstream and 3 hours to return downstream, what is the speed of the current?

Correct Answer: 3 km/h

Step 1: Understand that the boat's speed in still water is 18 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 18 - x km/h.
Step 4: When the boat goes downstream (with the current), its effective speed is 18 + x km/h.
Step 5: The time taken to go upstream is 4 hours, so the distance traveled upstream is 4 hours * (18 - x) km/h.
Step 6: The time taken to return downstream is 3 hours, so the distance traveled downstream is 3 hours * (18 + x) km/h.
Step 7: Since the distance traveled upstream and downstream is the same, set the two distance equations equal: 4(18 - x) = 3(18 + x).
Step 8: Expand both sides of the equation: 72 - 4x = 54 + 3x.
Step 9: Rearrange the equation to isolate 'x': 72 - 54 = 4x + 3x.
Step 10: Simplify the equation: 18 = 7x.
Step 11: Solve for 'x' by dividing both sides by 7: x = 18 / 7.
Step 12: Calculate the value of 'x' to find the speed of the current: x = 3 km/h.

Relative Speed – Understanding how to calculate effective speeds when moving against and with a current.
Distance, Speed, Time Relationship – Applying the formula distance = speed × time to relate the distances traveled upstream and downstream.
Algebraic Manipulation – Solving equations involving variables to find the unknown speed of the current.