A boat travels 40 km downstream and 30 km upstream in a total time of 6 hours. I

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What’s inside this PDF?

Question: A boat travels 40 km downstream and 30 km upstream in a total time of 6 hours. If the speed of the stream is 4 km/h, what is the speed of the boat in still water?

Options:

10 km/h
12 km/h
14 km/h
16 km/h

Correct Answer: 12 km/h

Solution:

Let speed of boat = x km/h. Time downstream = 40 / (x + 4) and time upstream = 30 / (x - 4). Thus, (40 / (x + 4)) + (30 / (x - 4)) = 6. Solving gives x = 14 km/h.

A boat travels 40 km downstream and 30 km upstream in a total time of 6 hours. I

Practice Questions

A boat travels 40 km downstream and 30 km upstream in a total time of 6 hours. If the speed of the stream is 4 km/h, what is the speed of the boat in still water?

10 km/h
12 km/h
14 km/h
16 km/h

Questions & Step-by-Step Solutions

A boat travels 40 km downstream and 30 km upstream in a total time of 6 hours. If the speed of the stream is 4 km/h, what is the speed of the boat in still water?

Step 1: Understand the problem. A boat travels downstream (with the current) and upstream (against the current). We need to find the speed of the boat in still water.
Step 2: Define the variables. Let the speed of the boat in still water be 'x' km/h.
Step 3: Determine the speed of the boat downstream. When the boat is going downstream, the speed is (x + 4) km/h because the stream adds to the boat's speed.
Step 4: Determine the speed of the boat upstream. When the boat is going upstream, the speed is (x - 4) km/h because the stream subtracts from the boat's speed.
Step 5: Calculate the time taken for each part of the journey. The time taken to travel downstream 40 km is 40 / (x + 4) hours. The time taken to travel upstream 30 km is 30 / (x - 4) hours.
Step 6: Set up the equation. The total time for both journeys is 6 hours, so we write the equation: (40 / (x + 4)) + (30 / (x - 4)) = 6.
Step 7: Solve the equation. To find 'x', we need to solve the equation from Step 6.
Step 8: After solving the equation, we find that x = 14 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 downstream and upstream.
Time Calculation – Using the formula time = distance/speed to calculate the time taken for each leg of the journey.
Algebraic Manipulation – Setting up and solving equations to find the unknown variable (speed of the boat in still water).

A boat travels 40 km downstream and 30 km upstream in a total time of 6 hours. I

What’s inside this PDF?

A boat travels 40 km downstream and 30 km upstream in a total time of 6 hours. I

Practice Questions

Questions & Step-by-Step Solutions

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