A boat travels 15 km upstream and 15 km downstream in a total time of 3 hours. I

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Question: A boat travels 15 km upstream and 15 km downstream in a total time of 3 hours. If the speed of the stream is 3 km/h, what is the speed of the boat in still water?

Options:

9 km/h
10 km/h
12 km/h
15 km/h

Correct Answer: 10 km/h

Solution:

Let speed of boat = x km/h. Time upstream = 15 / (x - 3) and downstream = 15 / (x + 3). Total time = 15/(x-3) + 15/(x+3) = 3. Solving gives x = 9 km/h.

A boat travels 15 km upstream and 15 km downstream in a total time of 3 hours. I

Practice Questions

A boat travels 15 km upstream and 15 km downstream in a total time of 3 hours. If the speed of the stream is 3 km/h, what is the speed of the boat in still water?

9 km/h
10 km/h
12 km/h
15 km/h

Questions & Step-by-Step Solutions

A boat travels 15 km upstream and 15 km downstream in a total time of 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. A boat travels 15 km upstream and 15 km downstream in a total of 3 hours.
Step 2: Know the speed of the stream. The speed of the stream is given as 3 km/h.
Step 3: Define the speed of the boat in still water. Let the speed of the boat be 'x' km/h.
Step 4: Calculate the effective speed of the boat upstream. When going upstream, the boat's speed is reduced by the speed of the stream: (x - 3) km/h.
Step 5: Calculate the effective speed of the boat downstream. When going downstream, the boat's speed is increased by the speed of the stream: (x + 3) km/h.
Step 6: Write the formula for time taken to travel upstream. Time upstream = Distance / Speed = 15 / (x - 3).
Step 7: Write the formula for time taken to travel downstream. Time downstream = Distance / Speed = 15 / (x + 3).
Step 8: Set up the equation for total time. The total time for both upstream and downstream is 3 hours: 15/(x - 3) + 15/(x + 3) = 3.
Step 9: Solve the equation. Multiply through by (x - 3)(x + 3) to eliminate the denominators and simplify the equation.
Step 10: Rearrange and solve for 'x'. After solving, you will find that x = 9 km/h.
Step 11: Conclusion. The speed of the boat in still water is 9 km/h.

Relative Speed – Understanding how the speed of the boat and the speed of the stream affect the effective speed when traveling upstream and downstream.
Time Calculation – Using the formula for time, which is distance divided by speed, to set up equations based on the given conditions.
Algebraic Manipulation – Solving equations involving fractions and finding a common denominator to simplify the problem.

A boat travels 15 km upstream and 15 km downstream in a total time of 3 hours. I

What’s inside this PDF?

A boat travels 15 km upstream and 15 km downstream in a total time of 3 hours. I

Practice Questions

Questions & Step-by-Step Solutions

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