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A boat can travel at 10 km/h in still water. If it takes 2 hours to go upstream

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Question: A boat can travel at 10 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. 2 km/h
  2. 3 km/h
  3. 4 km/h
  4. 5 km/h

Correct Answer: 3 km/h

Solution: 

Let the speed of the current be x. Upstream speed = 10 - x, Downstream speed = 10 + x. Time upstream = 2 hours, Time downstream = 1 hour. Thus, 2(10 - x) = Distance and 1(10 + x) = Distance. Equating gives x = 3 km/h.

A boat can travel at 10 km/h in still water. If it takes 2 hours to go upstream

Practice Questions

Q1
A boat can travel at 10 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. 2 km/h
  2. 3 km/h
  3. 4 km/h
  4. 5 km/h

Questions & Step-by-Step Solutions

A boat can travel at 10 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?
Correct Answer: 3 km/h
  • Step 1: Understand that the boat's speed in still water is 10 km/h.
  • Step 2: Define the speed of the current as 'x'.
  • Step 3: Calculate the upstream speed: Upstream speed = Boat speed - Current speed = 10 - x.
  • Step 4: Calculate the downstream speed: Downstream speed = Boat speed + Current speed = 10 + x.
  • Step 5: Note that it takes 2 hours to go upstream and 1 hour to return downstream.
  • Step 6: Use the formula: Distance = Speed × Time. For upstream, Distance = (10 - x) × 2.
  • Step 7: For downstream, Distance = (10 + x) × 1.
  • Step 8: Since the distance is the same for both trips, set the two distance equations equal: 2(10 - x) = 1(10 + x).
  • Step 9: Simplify the equation: 20 - 2x = 10 + x.
  • Step 10: Rearrange the equation to solve for x: 20 - 10 = 2x + x, which simplifies to 10 = 3x.
  • Step 11: Divide both sides by 3 to find x: x = 10 / 3, which equals approximately 3.33 km/h.
  • Step 12: Conclude that the speed of the current is approximately 3 km/h.
  • Relative Speed – Understanding how to calculate effective speeds when dealing with currents in water.
  • Time-Distance Relationship – Applying the relationship between time, speed, and distance to solve for unknowns.
  • Algebraic Equations – Setting up and solving equations based on given conditions.
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