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

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Question: 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?

Options:

  1. 3 km/h
  2. 4 km/h
  3. 5 km/h
  4. 6 km/h

Correct Answer: 5 km/h

Solution: 

Let speed of current = x. Upstream speed = 15 - x, Downstream speed = 15 + x. Distance = speed × time. 2(15 - x) = 1(15 + x). Solving gives x = 5 km/h.

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

Practice Questions

Q1
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?
  1. 3 km/h
  2. 4 km/h
  3. 5 km/h
  4. 6 km/h

Questions & Step-by-Step Solutions

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.
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