A boat takes 10 hours to go 40 km upstream and 8 hours to return downstream. Wha

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Question: A boat takes 10 hours to go 40 km upstream and 8 hours to return downstream. What is the speed of the stream?

Options:

1 km/h
2 km/h
3 km/h
4 km/h

Correct Answer: 2 km/h

Solution:

Speed upstream = 40 km / 10 h = 4 km/h. Speed downstream = 40 km / 8 h = 5 km/h. Let speed of boat = x, then x - s = 4 and x + s = 5. Solving gives s = 1 km/h.

A boat takes 10 hours to go 40 km upstream and 8 hours to return downstream. Wha

Practice Questions

A boat takes 10 hours to go 40 km upstream and 8 hours to return downstream. What is the speed of the stream?

1 km/h
2 km/h
3 km/h
4 km/h

Questions & Step-by-Step Solutions

A boat takes 10 hours to go 40 km upstream and 8 hours to return downstream. What is the speed of the stream?

Step 1: Understand that the boat travels upstream and downstream. Upstream means against the current, and downstream means with the current.
Step 2: Calculate the speed of the boat going upstream. The boat takes 10 hours to go 40 km upstream. So, speed upstream = distance / time = 40 km / 10 h = 4 km/h.
Step 3: Calculate the speed of the boat going downstream. The boat takes 8 hours to return 40 km downstream. So, speed downstream = distance / time = 40 km / 8 h = 5 km/h.
Step 4: Let the speed of the boat in still water be 'x' km/h and the speed of the stream be 's' km/h.
Step 5: Write the equations based on the speeds: For upstream, the effective speed is (x - s) = 4 km/h. For downstream, the effective speed is (x + s) = 5 km/h.
Step 6: Now you have two equations: x - s = 4 and x + s = 5.
Step 7: Solve these two equations. From the first equation, you can express x as x = s + 4. Substitute this into the second equation: (s + 4) + s = 5.
Step 8: Simplify the equation: 2s + 4 = 5. Subtract 4 from both sides: 2s = 1.
Step 9: Divide both sides by 2 to find s: s = 1 km/h.
Step 10: Conclude that the speed of the stream is 1 km/h.

Relative Speed – Understanding how the speed of a boat is affected by the speed of the stream when moving upstream and downstream.
Algebraic Equations – Setting up and solving equations based on the relationship between the speed of the boat, the speed of the stream, and the effective speeds upstream and downstream.
Time, Distance, and Speed Relationship – Applying the formula that relates time, distance, and speed to calculate the speeds in different scenarios.

A boat takes 10 hours to go 40 km upstream and 8 hours to return downstream. Wha

What’s inside this PDF?

A boat takes 10 hours to go 40 km upstream and 8 hours to return downstream. Wha

Practice Questions

Questions & Step-by-Step Solutions

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