Read the word problem below. Chan rows at a rate of eight miles per hour in still water. On Wednesday, it takes him three hours to row upstream from his house to the park. He rows back home, and it takes him two hours. What is the speed of the current? Which of the following is a clue that would help solve this word problem? The rate of Chan’s rowing in still water is 8 mph. Chan rows from the house to the park on Wednesday. Chan’s house is next to a river. The entire trip takes five hours.
Answers
A clue that would help to find the speed of the current is that the rate of Chan's rowing in still water is 8 mph.
Concept of Boat and Stream:
This concept comprises of 4 terminologies:
- Stream: Flowing water of the river is stream.
- Upstream: Direction of the boat is opposite to the flow of stream.
- Downstream: Direction of the boat is with the flow of stream.
- Still Water: Considering no movement of water, hence zero speed.
Given:
Speed of Chan's boat in stillwater = 8 mph
Time taken by Chan to row upstream from his house to the park = 3 h
Time taken by Chan to row downstream from the park to his house = 2 h
we have to find the speed of the current.
Let the speed of the current be v.
We know, Speed = Distance / Time
⇒ Distance = Speed × Time
Now, the distance between the house and the park is constant, hence the distance travelled upstream and downstream will be constant.
For upstream, speed of the boat is calculated as:
⇒ Speed = (speed of the boat in still water) - (speed of the current)
⇒ Speed = (8 - v)
Hence, distance is:
⇒ Distance = (8 - v) × 3 …(1)
Similarly for downstream, speed of the boat is:
⇒ Speed = (speed of the boat in still water) + (speed of the current)
⇒ Speed = (8 + v)
Distance will be:
⇒ Distance = (8 + v) × 2 …(2)
Now since the distance is equal we can equate the equation (1) and (2).
⇒ (8 - v) × 3 = (8 + v) × 2
⇒ 24 - 3v = 16 + 2v
⇒ 5v = 8
⇒ v = 1.6 mph
Hence, the speed of the current is 1.6 mph.
Here, we can observe that to solve this problem we need the time taken to cross along each stream and the speed of the boat in the still water.
The option: Chan rows from house to the park on Wednesday, gives information about the the distance travelled by the boat and it is constant and cannot be used to deduce the speed of the current.
The option: The entire trip takes five hours, is not used anywhere to solve the problem, instead the separate times to cross each stream was required. Hence this option was also not sufficient.
Therefore, the rate of Chan's rowing in still water is 8 mph, is the clue that helps to solve this word problem.
Learn more about the Boat and Stream Concept here: brainly.com/question/16712505?referrer=searchResults
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Answer:
its A
Step-by-step explanation:
i literally just took the test
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Hope this helps! :)
(Mark as Brainliest answer! Thanks!):)
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There is no possible combination that satisfy the given system of equations.
What is function?
A function is a relation between a dependent and independent variable.
Mathematically, we can write → y = f(x) = ax + b.
Given is to find what adds up to 12 but multiplies to 60.
We can write -
x + y = 12
xy = 60
Refer to the graph. The lines do not intersect. So, there is no possible combination that satisfy the given system of equations.
Therefore, there is no possible combination that satisfy the given system of equations.
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If equation one is multiplied by 2 and then the equations are added, the result is _____.
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X+2y=-1
I think you mean subtract the two.
That would get rid of the the y
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Step-by-step explanation:
Answers
Answer:
Step-by-step explanation:
To prove the straight line is tangent to the circle:
- substitute the straight line into the circle equation
- discriminant of the new equation has to be equals to 0
(1)
substitute x = 2y + 5 into x² + y² = 5
x² + y² = 5
(2y + 5)² + y² = 5
4y² + 20y + 25 + y² = 5
5y² + 20y + 20 = 0
y² + 4y + 4 = 0
(2)
discriminant of y² + 4y + 4 = 0 has to be equals to 0
D = 4² - 4(1)(4)
D = 0
∴ Proven