A boat travels 30 km downstream and returns upstream in a total time of 5 hours.

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What’s inside this PDF?

Question: A boat travels 30 km downstream and returns upstream in a total time of 5 hours. If the speed of the stream is 2 km/h, what is the speed of the boat in still water?

Options:

8 km/h
10 km/h
12 km/h
14 km/h

Correct Answer: 10 km/h

Solution:

Let speed of boat = x km/h. Time downstream = 30/(x+2) and upstream = 30/(x-2). Total time = 30/(x+2) + 30/(x-2) = 5. Solving gives x = 10 km/h.

A boat travels 30 km downstream and returns upstream in a total time of 5 hours.

Practice Questions

A boat travels 30 km downstream and returns upstream in a total time of 5 hours. If the speed of the stream is 2 km/h, what is the speed of the boat in still water?

8 km/h
10 km/h
12 km/h
14 km/h

Questions & Step-by-Step Solutions

A boat travels 30 km downstream and returns upstream in a total time of 5 hours. If the speed of the stream is 2 km/h, what is the speed of the boat in still water?

Step 1: Understand the problem. A boat travels 30 km downstream and then returns upstream, taking a total of 5 hours.
Step 2: Identify the speed of the stream, which is given as 2 km/h.
Step 3: Let the speed of the boat in still water be 'x' km/h.
Step 4: Calculate the speed of the boat downstream. This is the speed of the boat plus the speed of the stream: (x + 2) km/h.
Step 5: Calculate the time taken to travel downstream. Time = Distance / Speed, so time downstream = 30 / (x + 2) hours.
Step 6: Calculate the speed of the boat upstream. This is the speed of the boat minus the speed of the stream: (x - 2) km/h.
Step 7: Calculate the time taken to travel upstream. Time upstream = 30 / (x - 2) hours.
Step 8: Set up the equation for total time. The total time for both trips is 5 hours: 30 / (x + 2) + 30 / (x - 2) = 5.
Step 9: Solve the equation from Step 8 to find the value of 'x'.
Step 10: After solving, you find that x = 10 km/h, which is the speed of the boat in still water.

Relative Speed – Understanding how the speed of the stream affects the effective speed of the boat when traveling downstream and upstream.
Time Calculation – Using the formula time = distance/speed to calculate the time taken for both downstream and upstream journeys.
Algebraic Manipulation – Setting up and solving equations to find the unknown speed of the boat.

A boat travels 30 km downstream and returns upstream in a total time of 5 hours.

What’s inside this PDF?

A boat travels 30 km downstream and returns upstream in a total time of 5 hours.

Practice Questions

Questions & Step-by-Step Solutions

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