Math Problem Statement
The speed of a boat in still water is 9 km/h. Length of the river is 36 km. The boat takes 9 hours to go and come back. Find the speed of the stream.
Solution
Let's solve the problem step-by-step.
Given:
- Speed of the boat in still water: km/hr.
- Distance of the river (one way): km.
- Total time taken for the journey (going and coming back): hours.
To Find:
- Speed of the stream .
Steps to Solve:
-
Define the Speeds in Each Direction:
-
Downstream speed (going with the stream):
The speed of the boat downstream is the sum of the boat's speed in still water and the stream's speed: -
Upstream speed (going against the stream):
The speed of the boat upstream is the difference between the boat's speed in still water and the stream's speed:
-
-
Calculate Time for Each Leg of the Journey:
-
Time taken downstream (from start to end of river):
-
Time taken upstream (from end back to start):
-
-
Set Up the Total Time Equation:
The total time for the journey (going downstream and coming back upstream) is the sum of both times: Substituting the expressions for and :
-
Solve for :
First, divide the entire equation by 9 to simplify:
Clear the denominators by multiplying through by :
Expand both sides:
Combine like terms:
Rearrange to isolate :
Take the square root of both sides:
Answer:
The speed of the stream is 3 km/hr.
Would you like more details or have any questions about this solution?
Here are some related questions for further exploration:
- What would be the total time taken if the speed of the stream increased to 4 km/hr?
- How would the total journey time change if the river length was doubled to 72 km?
- If the boat took 10 hours instead of 9 hours for the same journey, what would the stream's speed be?
- Can you determine the speed of the boat in still water if the stream's speed was 5 km/hr and the total time was 8 hours?
- What happens to the upstream time if the stream's speed equals the boat's speed in still water?
Tip: When solving problems involving relative motion in water, always distinguish between upstream and downstream conditions to avoid confusion.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Speed, Distance, and Time Calculations
Relative Motion in Rivers
Formulas
Time = Distance / Speed
Speed of Boat in Still Water = Downstream Speed - Stream Speed
Speed of Boat in Still Water = Upstream Speed + Stream Speed
Theorems
-
Suitable Grade Level
Grades 9-12