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A boat can go 15 km upstream and 21 km downstream in 3 hours. If the speed of th

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Question: A boat can go 15 km upstream and 21 km downstream in 3 hours. If the speed of the stream is 3 km/h, what is the speed of the boat in still water?

Options:

  1. 6 km/h
  2. 9 km/h
  3. 12 km/h
  4. 15 km/h

Correct Answer: 9 km/h

Solution: 

Let the speed of the boat in still water be x km/h. The speed upstream = (x - 3) km/h and downstream = (x + 3) km/h. Time taken upstream = 15/(x - 3) and downstream = 21/(x + 3). Therefore, (15/(x - 3)) + (21/(x + 3)) = 3. Solving gives x = 9 km/h.

A boat can go 15 km upstream and 21 km downstream in 3 hours. If the speed of th

Practice Questions

Q1
A boat can go 15 km upstream and 21 km downstream in 3 hours. If the speed of the stream is 3 km/h, what is the speed of the boat in still water?
  1. 6 km/h
  2. 9 km/h
  3. 12 km/h
  4. 15 km/h

Questions & Step-by-Step Solutions

A boat can go 15 km upstream and 21 km downstream in 3 hours. If the speed of the stream is 3 km/h, what is the speed of the boat in still water?
  • Step 1: Understand the problem. We need to find the speed of the boat in still water, which we will call 'x' km/h.
  • Step 2: Know the speed of the stream. The speed of the stream is given as 3 km/h.
  • Step 3: Determine the speed of the boat when going upstream and downstream. When going upstream (against the stream), the speed is (x - 3) km/h. When going downstream (with the stream), the speed is (x + 3) km/h.
  • Step 4: Write down the distances traveled. The boat goes 15 km upstream and 21 km downstream.
  • Step 5: Calculate the time taken for each part of the journey. The time taken to go upstream is 15/(x - 3) hours, and the time taken to go downstream is 21/(x + 3) hours.
  • Step 6: Set up the equation for total time. The total time for both journeys is 3 hours, so we write the equation: (15/(x - 3)) + (21/(x + 3)) = 3.
  • Step 7: Solve the equation. To find 'x', we need to solve the equation we set up in Step 6.
  • Step 8: After solving the equation, we find that x = 9 km/h. This is the speed of the boat in still water.
  • Relative Speed – Understanding how the speed of the boat is affected by the speed of the stream when traveling upstream and downstream.
  • Time-Distance Relationship – Applying the relationship between speed, distance, and time to set up equations for the problem.
  • Algebraic Manipulation – Solving equations involving fractions to find the unknown variable (speed of the boat).
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