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Please give equation for this question--- a motor boat goes 10 km upstream and returns back to the starting point in 55 minutes. if the speed of the boat in still water is 22 km per hour find the speed of current?
Verified Answer
Please give equation for this question--- a motor boat goes 10 km upst...
Let speed of motor boat = x
downstream speed = x + 2
upstream speed = x - 2
so,
10/(x + 2)+10/(x - 2) = 55/60
55x^2-1200x-220
x=22 answer
This question is part of UPSC exam. View all Class 10 courses
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Please give equation for this question--- a motor boat goes 10 km upst...
Problem Analysis:
Let's break down the problem to understand it better:
- The boat travels 10 km upstream.
- It then returns to the starting point.
- The total time taken for the round trip is 55 minutes.
- The speed of the boat in still water is 22 km/h.
Understanding the Terms:
- Speed of the boat in still water: This refers to the speed at which the boat would travel if there were no current. It represents the relative speed of the boat with respect to the water.
- Speed of the current: This refers to the speed of the water flow. It affects the actual speed of the boat when it's moving upstream or downstream.
Calculating the Speed of the Boat:
Let's assume the speed of the current is 'c' km/h.
When the boat is moving upstream:
- The effective speed of the boat is reduced by the speed of the current, resulting in a slower speed relative to the ground.
- The time taken to cover the distance of 10 km upstream can be calculated using the formula: time = distance / speed.
- The speed of the boat while moving upstream will be (22 - c) km/h.
When the boat is moving downstream:
- The effective speed of the boat is increased by the speed of the current, resulting in a faster speed relative to the ground.
- The time taken to cover the distance of 10 km downstream can be calculated using the formula: time = distance / speed.
- The speed of the boat while moving downstream will be (22 + c) km/h.
Equation:
According to the problem, the total time taken for the round trip is 55 minutes or 55/60 hours.
So, the equation for the total time taken is:
10 / (22 - c) + 10 / (22 + c) = 55/60.
Now, we can solve this equation to find the value of 'c', which represents the speed of the current.
Let's break down the problem to understand it better:
- The boat travels 10 km upstream.
- It then returns to the starting point.
- The total time taken for the round trip is 55 minutes.
- The speed of the boat in still water is 22 km/h.
Understanding the Terms:
- Speed of the boat in still water: This refers to the speed at which the boat would travel if there were no current. It represents the relative speed of the boat with respect to the water.
- Speed of the current: This refers to the speed of the water flow. It affects the actual speed of the boat when it's moving upstream or downstream.
Calculating the Speed of the Boat:
Let's assume the speed of the current is 'c' km/h.
When the boat is moving upstream:
- The effective speed of the boat is reduced by the speed of the current, resulting in a slower speed relative to the ground.
- The time taken to cover the distance of 10 km upstream can be calculated using the formula: time = distance / speed.
- The speed of the boat while moving upstream will be (22 - c) km/h.
When the boat is moving downstream:
- The effective speed of the boat is increased by the speed of the current, resulting in a faster speed relative to the ground.
- The time taken to cover the distance of 10 km downstream can be calculated using the formula: time = distance / speed.
- The speed of the boat while moving downstream will be (22 + c) km/h.
Equation:
According to the problem, the total time taken for the round trip is 55 minutes or 55/60 hours.
So, the equation for the total time taken is:
10 / (22 - c) + 10 / (22 + c) = 55/60.
Now, we can solve this equation to find the value of 'c', which represents the speed of the current.
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Please give equation for this question--- a motor boat goes 10 km upstream and returns back to the starting point in 55 minutes. if the speed of the boat in still water is 22 km per hour find the speed of current?
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Please give equation for this question--- a motor boat goes 10 km upstream and returns back to the starting point in 55 minutes. if the speed of the boat in still water is 22 km per hour find the speed of current? 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 Please give equation for this question--- a motor boat goes 10 km upstream and returns back to the starting point in 55 minutes. if the speed of the boat in still water is 22 km per hour find the speed of current? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Please give equation for this question--- a motor boat goes 10 km upstream and returns back to the starting point in 55 minutes. if the speed of the boat in still water is 22 km per hour find the speed of current?.
Please give equation for this question--- a motor boat goes 10 km upstream and returns back to the starting point in 55 minutes. if the speed of the boat in still water is 22 km per hour find the speed of current? 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 Please give equation for this question--- a motor boat goes 10 km upstream and returns back to the starting point in 55 minutes. if the speed of the boat in still water is 22 km per hour find the speed of current? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Please give equation for this question--- a motor boat goes 10 km upstream and returns back to the starting point in 55 minutes. if the speed of the boat in still water is 22 km per hour find the speed of current?.
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