A boat can travel at 15 km/h in still water. If it takes 2 hours to go upstream

A boat can travel at 15 km/h in still water. If it takes 2 hours to go upstream and 1 hour to return downstream, what is the speed of the current?

A boat can travel at 15 km/h in still water. If it takes 2 hours to go upstream and 1 hour to return downstream, what is the speed of the current?

Step 1: Understand that the boat's speed in still water is 15 km/h.
Step 2: Define the speed of the current as 'x'.
Step 3: Calculate the upstream speed: Upstream speed = Boat speed - Current speed = 15 - x.
Step 4: Calculate the downstream speed: Downstream speed = Boat speed + Current speed = 15 + x.
Step 5: Use the formula Distance = Speed × Time to set up equations for upstream and downstream.
Step 6: For upstream, the distance traveled in 2 hours is: Distance = (15 - x) × 2.
Step 7: For downstream, the distance traveled in 1 hour is: Distance = (15 + x) × 1.
Step 8: Since the distance is the same for both upstream and downstream, set the two distances equal: 2(15 - x) = 1(15 + x).
Step 9: Simplify the equation: 30 - 2x = 15 + x.
Step 10: Solve for 'x': Add 2x to both sides: 30 = 15 + 3x. Then subtract 15 from both sides: 15 = 3x. Finally, divide by 3: x = 5.
Step 11: Conclude that the speed of the current is 5 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 solve for unknowns.
Algebraic Manipulation – Solving equations involving variables to find the speed of the current.