A boat travels 20 km upstream and 30 km downstream in a total time of 5 hours. I

₹0.0

📥 Instant PDF Download
♾ Lifetime Access
🛡 Secure & Original Content

What’s inside this PDF?

Question: A boat travels 20 km upstream and 30 km downstream 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 upstream = 20 / (x - 2) and time downstream = 30 / (x + 2). Thus, (20 / (x - 2)) + (30 / (x + 2)) = 5. Solving gives x = 12 km/h.

A boat travels 20 km upstream and 30 km downstream in a total time of 5 hours. I

Practice Questions

A boat travels 20 km upstream and 30 km downstream 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 20 km upstream and 30 km downstream 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. We have a boat that travels upstream and downstream. 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 when going upstream. When the boat goes upstream, it moves against the stream, so its effective speed is (x - 2) km/h.
Step 4: Determine the speed of the boat when going downstream. When the boat goes downstream, it moves with the stream, so its effective speed is (x + 2) km/h.
Step 5: Calculate the time taken to travel upstream. The time taken to travel 20 km upstream is given by the formula: time = distance / speed. So, time upstream = 20 / (x - 2).
Step 6: Calculate the time taken to travel downstream. The time taken to travel 30 km downstream is given by the formula: time = distance / speed. So, time downstream = 30 / (x + 2).
Step 7: Set up the equation for total time. The total time for both trips is 5 hours, so we can write the equation: (20 / (x - 2)) + (30 / (x + 2)) = 5.
Step 8: Solve the equation. To find 'x', we need to solve the equation from Step 7.
Step 9: After solving the equation, we find that x = 12 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 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 20 km upstream and 30 km downstream in a total time of 5 hours. I

What’s inside this PDF?

A boat travels 20 km upstream and 30 km downstream in a total time of 5 hours. I

Practice Questions

Questions & Step-by-Step Solutions

On a scale of 0–10, how likely are you to recommend The Soulshift Academy?