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A boat can travel at 12 km/h in still water. If it takes 3 hours to go upstream

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Question: A boat can travel at 12 km/h in still water. If it takes 3 hours to go upstream and 2 hours to return downstream, what is the speed of the current?

Options:

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

Correct Answer: 2 km/h

Solution: 

Let the speed of the current be x. Upstream speed = 12 - x, Downstream speed = 12 + x. Distance = 3(12 - x) = 2(12 + x). Solving gives x = 2 km/h.

A boat can travel at 12 km/h in still water. If it takes 3 hours to go upstream

Practice Questions

Q1
A boat can travel at 12 km/h in still water. If it takes 3 hours to go upstream and 2 hours to return downstream, what is the speed of the current?
  1. 1 km/h
  2. 2 km/h
  3. 3 km/h
  4. 4 km/h

Questions & Step-by-Step Solutions

A boat can travel at 12 km/h in still water. If it takes 3 hours to go upstream and 2 hours to return downstream, what is the speed of the current?
Correct Answer: 2 km/h
  • Step 1: Understand that the boat's speed in still water is 12 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 12 - x km/h.
  • Step 4: When the boat goes downstream (with the current), its effective speed is 12 + x km/h.
  • Step 5: The time taken to go upstream is 3 hours, so the distance traveled upstream is 3 hours * (12 - x) km/h.
  • Step 6: The time taken to return downstream is 2 hours, so the distance traveled downstream is 2 hours * (12 + x) km/h.
  • Step 7: Since the distance traveled upstream and downstream is the same, set the two distance equations equal: 3(12 - x) = 2(12 + x).
  • Step 8: Expand both sides of the equation: 36 - 3x = 24 + 2x.
  • Step 9: Rearrange the equation to isolate 'x': 36 - 24 = 3x + 2x.
  • Step 10: Combine like terms: 12 = 5x.
  • Step 11: Solve for 'x' by dividing both sides by 5: x = 12 / 5 = 2.4 km/h.
  • Step 12: Conclude that the speed of the current is 2 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 set up equations for upstream and downstream travel.
  • Algebraic Manipulation – Solving equations to find the unknown variable, in this case, the speed of the current.
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