A boat travels upstream at 4 km/h and downstream at 6 km/h. What is the speed of

A boat travels upstream at 4 km/h and downstream at 6 km/h. What is the speed of the current?

A boat travels upstream at 4 km/h and downstream at 6 km/h. What is the speed of the current?

Correct Answer: 2 km/h

Step 1: Understand that the boat's speed upstream is affected by the current. The speed of the boat upstream is 4 km/h.
Step 2: Understand that the boat's speed downstream is helped by the current. The speed of the boat downstream is 6 km/h.
Step 3: Let the speed of the current be represented by 'x'.
Step 4: Write an equation for the upstream speed: The boat's speed upstream (4 km/h) is equal to the speed of the boat in still water (which is the speed of the boat downstream minus the current). So, 4 + x = 6 - x.
Step 5: Rearrange the equation to solve for 'x'. Add 'x' to both sides: 4 + x + x = 6. This simplifies to 4 + 2x = 6.
Step 6: Subtract 4 from both sides: 2x = 6 - 4, which simplifies to 2x = 2.
Step 7: Divide both sides by 2 to find 'x': x = 2 km/h.
Step 8: Conclude that the speed of the current is 2 km/h.

Relative Speed – Understanding how the speed of a boat is affected by the current when traveling upstream and downstream.
Algebraic Manipulation – Using algebra to set up and solve equations based on the relationship between the speeds.