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A boat covers 8km in 40 minutes while travelling down stream it takes 1 hr to take return journey if speed of boat and flow of river are uniform find speed of boat in still water and speed of stream?
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A boat covers 8km in 40 minutes while travelling down stream it takes ...
We have a boat covers 8 km in 40 min, while travelling downstream, but takes 1 hr to make the return journey, if the speed of the boat and flow of river is uniform, find the speed of the boat in still water and speed of the stream.
As it is given speed of river & boat are uniform
⇒let speed of boat in still water=u km/h
⇒let speed of river =v km/h
In downstream boat floats in direction of river flow, their speeds add up, speed of boat=(u+v) km/h
In upstream boat floats in opposite direction of river flow,their speeds=boat speed −river speed
⇒speed of boat=(u−v) km/h x [in return distance would be 8 km only]
Distance covered in downstream = 8 km
⇒speed x time = 8
⇒(u + v)4060 = 8
⇒u + v = 12 ...(1)
Distance covered in upstream = 8 km
⇒(u − v) x 1 = 8
⇒u − v = 8 ...(2)
Add (1) and (2), we get
2u = 20
⇒u = 10 km/h
Now, from (1), we get
v = 2 km/h
Speed of boat = 10 km/h
speed of river = 2 km/h
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Most Upvoted Answer
A boat covers 8km in 40 minutes while travelling down stream it takes ...
Given Information:
- Distance covered downstream = 8 km
- Time taken downstream = 40 minutes = 40/60 hours = 2/3 hours
- Time taken for the return journey = 1 hour
Let's assume:
- Speed of the boat in still water = x km/h
- Speed of the stream = y km/h
Calculating Speed:
- Downstream speed = (Speed of boat in still water) + (Speed of stream)
- Upstream speed = (Speed of boat in still water) - (Speed of stream)
Calculating Distance:
- Distance = Speed × Time
Calculating Downstream Speed:
- Distance covered downstream = Downstream speed × Time taken downstream
- 8 = (x + y) × (2/3)
- 24 = 2x + 2y [Multiplying both sides by 3 to eliminate the fraction]
Calculating Upstream Speed:
- Distance covered upstream = Upstream speed × Time taken for the return journey
- 8 = (x - y) × 1
- 8 = x - y [Simplifying]
Solving the Equations:
Now we have two equations:
- 2x + 2y = 24
- x - y = 8
Multiplying the second equation by 2:
- 2(x - y) = 2 × 8
- 2x - 2y = 16
Adding the two equations:
- (2x + 2y) + (2x - 2y) = 24 + 16
- 4x = 40
Dividing both sides by 4:
- x = 10
Calculating Speed of Stream:
- Substituting the value of x in the second equation:
- 10 - y = 8
- y = 10 - 8
- y = 2
Hence, the speed of the boat in still water is 10 km/h and the speed of the stream is 2 km/h.
- Distance covered downstream = 8 km
- Time taken downstream = 40 minutes = 40/60 hours = 2/3 hours
- Time taken for the return journey = 1 hour
Let's assume:
- Speed of the boat in still water = x km/h
- Speed of the stream = y km/h
Calculating Speed:
- Downstream speed = (Speed of boat in still water) + (Speed of stream)
- Upstream speed = (Speed of boat in still water) - (Speed of stream)
Calculating Distance:
- Distance = Speed × Time
Calculating Downstream Speed:
- Distance covered downstream = Downstream speed × Time taken downstream
- 8 = (x + y) × (2/3)
- 24 = 2x + 2y [Multiplying both sides by 3 to eliminate the fraction]
Calculating Upstream Speed:
- Distance covered upstream = Upstream speed × Time taken for the return journey
- 8 = (x - y) × 1
- 8 = x - y [Simplifying]
Solving the Equations:
Now we have two equations:
- 2x + 2y = 24
- x - y = 8
Multiplying the second equation by 2:
- 2(x - y) = 2 × 8
- 2x - 2y = 16
Adding the two equations:
- (2x + 2y) + (2x - 2y) = 24 + 16
- 4x = 40
Dividing both sides by 4:
- x = 10
Calculating Speed of Stream:
- Substituting the value of x in the second equation:
- 10 - y = 8
- y = 10 - 8
- y = 2
Hence, the speed of the boat in still water is 10 km/h and the speed of the stream is 2 km/h.
Community Answer
A boat covers 8km in 40 minutes while travelling down stream it takes ...
10 km /m 2 km /h
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A boat covers 8km in 40 minutes while travelling down stream it takes 1 hr to take return journey if speed of boat and flow of river are uniform find speed of boat in still water and speed of stream?
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A boat covers 8km in 40 minutes while travelling down stream it takes 1 hr to take return journey if speed of boat and flow of river are uniform find speed of boat in still water and speed of stream? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about A boat covers 8km in 40 minutes while travelling down stream it takes 1 hr to take return journey if speed of boat and flow of river are uniform find speed of boat in still water and speed of stream? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A boat covers 8km in 40 minutes while travelling down stream it takes 1 hr to take return journey if speed of boat and flow of river are uniform find speed of boat in still water and speed of stream?.
A boat covers 8km in 40 minutes while travelling down stream it takes 1 hr to take return journey if speed of boat and flow of river are uniform find speed of boat in still water and speed of stream? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about A boat covers 8km in 40 minutes while travelling down stream it takes 1 hr to take return journey if speed of boat and flow of river are uniform find speed of boat in still water and speed of stream? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A boat covers 8km in 40 minutes while travelling down stream it takes 1 hr to take return journey if speed of boat and flow of river are uniform find speed of boat in still water and speed of stream?.
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