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A boat travels 30 km upstream in the same amount of time it takes to travel 60 km downstream in the river. If the speed of the river is 4 km/h , find the speed of the boat in still water?
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A boat travels 30 km upstream in the same amount of time it takes to t...
Problem:
A boat travels 30 km upstream in the same amount of time it takes to travel 60 km downstream in the river. If the speed of the river is 4 km/h, find the speed of the boat in still water?
Solution:
To solve this problem, we can use the concept of relative speed. Let's assume the speed of the boat in still water is 'b' km/h.
Speed Upstream:
When the boat travels upstream, it has to fight against the current of the river. The speed of the river is given as 4 km/h, so the effective speed of the boat when going upstream will be (b - 4) km/h.
Speed Downstream:
When the boat travels downstream, it gets an additional push from the current of the river. Therefore, the effective speed of the boat when going downstream will be (b + 4) km/h.
Time taken upstream:
We are given that the boat takes the same amount of time to travel 30 km upstream as it takes to travel 60 km downstream. Let's assume this common time as 't' hours.
The formula to calculate time is:
Time = Distance / Speed
So, the time taken to travel upstream is 30 / (b - 4) hours.
Time taken downstream:
The time taken to travel downstream is 60 / (b + 4) hours.
Since the time taken is the same in both cases, we can set up the following equation:
30 / (b - 4) = 60 / (b + 4)
Solving the equation:
To solve the equation, we can cross-multiply:
30 * (b + 4) = 60 * (b - 4)
30b + 120 = 60b - 240
30b - 60b = -240 - 120
-30b = -360
Dividing both sides by -30:
b = 12
Answer:
The speed of the boat in still water is 12 km/h.
A boat travels 30 km upstream in the same amount of time it takes to travel 60 km downstream in the river. If the speed of the river is 4 km/h, find the speed of the boat in still water?
Solution:
To solve this problem, we can use the concept of relative speed. Let's assume the speed of the boat in still water is 'b' km/h.
Speed Upstream:
When the boat travels upstream, it has to fight against the current of the river. The speed of the river is given as 4 km/h, so the effective speed of the boat when going upstream will be (b - 4) km/h.
Speed Downstream:
When the boat travels downstream, it gets an additional push from the current of the river. Therefore, the effective speed of the boat when going downstream will be (b + 4) km/h.
Time taken upstream:
We are given that the boat takes the same amount of time to travel 30 km upstream as it takes to travel 60 km downstream. Let's assume this common time as 't' hours.
The formula to calculate time is:
Time = Distance / Speed
So, the time taken to travel upstream is 30 / (b - 4) hours.
Time taken downstream:
The time taken to travel downstream is 60 / (b + 4) hours.
Since the time taken is the same in both cases, we can set up the following equation:
30 / (b - 4) = 60 / (b + 4)
Solving the equation:
To solve the equation, we can cross-multiply:
30 * (b + 4) = 60 * (b - 4)
30b + 120 = 60b - 240
30b - 60b = -240 - 120
-30b = -360
Dividing both sides by -30:
b = 12
Answer:
The speed of the boat in still water is 12 km/h.
Community Answer
A boat travels 30 km upstream in the same amount of time it takes to t...
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A boat travels 30 km upstream in the same amount of time it takes to travel 60 km downstream in the river. If the speed of the river is 4 km/h , find the speed of the boat in still water?
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A boat travels 30 km upstream in the same amount of time it takes to travel 60 km downstream in the river. If the speed of the river is 4 km/h , find the speed of the boat in still water? for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about A boat travels 30 km upstream in the same amount of time it takes to travel 60 km downstream in the river. If the speed of the river is 4 km/h , find the speed of the boat in still water? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A boat travels 30 km upstream in the same amount of time it takes to travel 60 km downstream in the river. If the speed of the river is 4 km/h , find the speed of the boat in still water?.
A boat travels 30 km upstream in the same amount of time it takes to travel 60 km downstream in the river. If the speed of the river is 4 km/h , find the speed of the boat in still water? for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about A boat travels 30 km upstream in the same amount of time it takes to travel 60 km downstream in the river. If the speed of the river is 4 km/h , find the speed of the boat in still water? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A boat travels 30 km upstream in the same amount of time it takes to travel 60 km downstream in the river. If the speed of the river is 4 km/h , find the speed of the boat in still water?.
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