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Swati can row her boat at a speed of 5 km/h in still water. If it takes her 1 hour more to row the boat 5.25 km upstream than to return downstream, find the speed of the stream.?
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Problem
Swati can row her boat at a speed of 5 km/h in still water. If it takes her 1 hour more to row the boat 5.25 km upstream than to return downstream, find the speed of the stream.
Solution
Let the speed of the stream be x km/h.
Speed of boat downstream
The speed of the boat downstream is the sum of the speed of the boat in still water and the speed of the stream.
Speed downstream = 5 + x km/h
Speed of boat upstream
The speed of the boat upstream is the difference between the speed of the boat in still water and the speed of the stream.
Speed upstream = 5 - x km/h
Time taken to row upstream
Let t be the time taken to row the boat upstream.
Distance = 5.25 km
Speed = Speed upstream = 5 - x km/h
Time = Distance/Speed = 5.25/(5-x) hours
Time taken to row downstream
The time taken to row the boat downstream is 1 hour less than the time taken to row upstream.
Time downstream = t - 1 hour
Distance covered downstream
The distance covered downstream is the same as the distance covered upstream.
Distance downstream = Distance upstream = 5.25 km
Speed downstream = 5 + x km/h
Time downstream = t - 1 hour
Distance downstream = Speed downstream × Time downstream
5.25 = (5 + x) × (t - 1)
5.25 = 5t + xt - 5 - x
6.25 = xt
t = 6.25/x
Substituting t = 6.25/x in the equation 5.25 = (5 + x) × (t - 1), we get:
5.25 = (5 + x) × (6.25/x - 1)
5.25 = 31.25/x - 5 - x
10.25 = 26.25/x
x = 2.56 km/h
Therefore, the speed of the stream is 2.56 km/h.
Swati can row her boat at a speed of 5 km/h in still water. If it takes her 1 hour more to row the boat 5.25 km upstream than to return downstream, find the speed of the stream.
Solution
Let the speed of the stream be x km/h.
Speed of boat downstream
The speed of the boat downstream is the sum of the speed of the boat in still water and the speed of the stream.
Speed downstream = 5 + x km/h
Speed of boat upstream
The speed of the boat upstream is the difference between the speed of the boat in still water and the speed of the stream.
Speed upstream = 5 - x km/h
Time taken to row upstream
Let t be the time taken to row the boat upstream.
Distance = 5.25 km
Speed = Speed upstream = 5 - x km/h
Time = Distance/Speed = 5.25/(5-x) hours
Time taken to row downstream
The time taken to row the boat downstream is 1 hour less than the time taken to row upstream.
Time downstream = t - 1 hour
Distance covered downstream
The distance covered downstream is the same as the distance covered upstream.
Distance downstream = Distance upstream = 5.25 km
Speed downstream = 5 + x km/h
Time downstream = t - 1 hour
Distance downstream = Speed downstream × Time downstream
5.25 = (5 + x) × (t - 1)
5.25 = 5t + xt - 5 - x
6.25 = xt
t = 6.25/x
Substituting t = 6.25/x in the equation 5.25 = (5 + x) × (t - 1), we get:
5.25 = (5 + x) × (6.25/x - 1)
5.25 = 31.25/x - 5 - x
10.25 = 26.25/x
x = 2.56 km/h
Therefore, the speed of the stream is 2.56 km/h.
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Swati can row her boat at a speed of 5 km/h in still water. If it takes her 1 hour more to row the boat 5.25 km upstream than to return downstream, find the speed of the stream.?
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Swati can row her boat at a speed of 5 km/h in still water. If it takes her 1 hour more to row the boat 5.25 km upstream than to return downstream, 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 Swati can row her boat at a speed of 5 km/h in still water. If it takes her 1 hour more to row the boat 5.25 km upstream than to return downstream, 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 Swati can row her boat at a speed of 5 km/h in still water. If it takes her 1 hour more to row the boat 5.25 km upstream than to return downstream, find the speed of the stream.?.
Swati can row her boat at a speed of 5 km/h in still water. If it takes her 1 hour more to row the boat 5.25 km upstream than to return downstream, 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 Swati can row her boat at a speed of 5 km/h in still water. If it takes her 1 hour more to row the boat 5.25 km upstream than to return downstream, 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 Swati can row her boat at a speed of 5 km/h in still water. If it takes her 1 hour more to row the boat 5.25 km upstream than to return downstream, find the speed of the stream.?.
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