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A boat whose speed in still water is 18 kilometre per hour takes 1 hour more to go 24 km upstream then to return downstream to the same spot find the speed of the stream?
Most Upvoted Answer
A boat whose speed in still water is 18 kilometre per hour takes 1 hou...
Let the speed of the stream be x km/hr.
Given: Time taken for going upstream is one hour more than the time taken for going downstream. So, tup=tdown+1 (A)
Distance upstream = Distance downstream = 24 km
Speed of the boat going upstream, vup=18−x
Speed of the boat going downstream, vdown=18+x
Time taken going upstream, tup=Distance upstreamSpeed upstream =2418−x
tup=2418−x (1)
Time taken going downstream, tdown=Distance downstreamSpeed downstream =2418+x
or tdown=2418+x (2)
Using equation (1), (2) and (A):
2418−x=2418+x+1
24(18+x)=24(18−x)+(18+x)(18−x)
24∗18+24x=24∗18−24x+182−x2
x2+48x−182=0
x2+54x−6x−324=0
(x+54)(x−6)=0
x =6 (Rejecting negative value of x)
Given: Time taken for going upstream is one hour more than the time taken for going downstream. So, tup=tdown+1 (A)
Distance upstream = Distance downstream = 24 km
Speed of the boat going upstream, vup=18−x
Speed of the boat going downstream, vdown=18+x
Time taken going upstream, tup=Distance upstreamSpeed upstream =2418−x
tup=2418−x (1)
Time taken going downstream, tdown=Distance downstreamSpeed downstream =2418+x
or tdown=2418+x (2)
Using equation (1), (2) and (A):
2418−x=2418+x+1
24(18+x)=24(18−x)+(18+x)(18−x)
24∗18+24x=24∗18−24x+182−x2
x2+48x−182=0
x2+54x−6x−324=0
(x+54)(x−6)=0
x =6 (Rejecting negative value of x)
Community Answer
A boat whose speed in still water is 18 kilometre per hour takes 1 hou...
Problem:
A boat whose speed in still water is 18 kilometre per hour takes 1 hour more to go 24 km upstream then to return downstream to the same spot find the speed of the stream?
Step 1: Understand the problem
The problem describes a boat that moves upstream and downstream at different speeds, which is affected by the speed of the stream. We need to find the speed of the stream.
Step 2: Formulate the equations
Let's assume the speed of the stream is x km/h.
Speed downstream = (18 + x) km/h
Speed upstream = (18 - x) km/h
Time taken upstream = Time taken downstream + 1 hour
Distance traveled upstream = Distance traveled downstream
Distance = Speed x Time
24 = (18 + x) x t1
24 = (18 - x) x (t1 + 1)
Step 3: Solve the equations
Let's solve the equations to find the value of x.
24/(18 + x) = t1
24/(18 - x) = t1 + 1
24 = t1(18 + x)
24 = (t1 + 1)(18 - x)
Substitute t1 from equation 1 to equation 3
24 = (24/(18 + x))(18 + x)
24 = 24
Substitute t1 from equation 2 to equation 4
24 = (24/(18 - x))(18 - x + 18)
24 = (24/(18 - x))(36)
18 - x = 12
x = 6 km/h
Step 4: Check the answer
Let's check the answer by substituting x = 6 in the equations.
Speed downstream = (18 + 6) = 24 km/h
Speed upstream = (18 - 6) = 12 km/h
Time taken downstream = 24/24 = 1 hour
Time taken upstream = 24/12 = 2 hours
Distance downstream = Speed downstream x Time = 24 x 1 = 24 km
Distance upstream = Speed upstream x Time = 12 x 2 = 24 km
The answer is correct.
Step 5: Conclusion
The speed of the stream is 6 km/h.
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A boat whose speed in still water is 18 kilometre per hour takes 1 hour more to go 24 km upstream then to return downstream to the same spot find the speed of the stream?
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A boat whose speed in still water is 18 kilometre per hour takes 1 hour more to go 24 km upstream then to return downstream to the same spot find the speed of the 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 whose speed in still water is 18 kilometre per hour takes 1 hour more to go 24 km upstream then to return downstream to the same spot find the speed of the stream? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A boat whose speed in still water is 18 kilometre per hour takes 1 hour more to go 24 km upstream then to return downstream to the same spot find the speed of the stream?.
A boat whose speed in still water is 18 kilometre per hour takes 1 hour more to go 24 km upstream then to return downstream to the same spot find the speed of the 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 whose speed in still water is 18 kilometre per hour takes 1 hour more to go 24 km upstream then to return downstream to the same spot find the speed of the stream? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A boat whose speed in still water is 18 kilometre per hour takes 1 hour more to go 24 km upstream then to return downstream to the same spot find the speed of the stream?.
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