What is the formula to calculate the speed of a boat in still water when given the speed of the current?
Acad Alg2 Rationals Review with Application Problems

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Mathematics
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11th Grade
•
Hard
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1.
FLASHCARD QUESTION
Front
Back
If a boat can row upstream at speed 'b' and downstream at speed 'b + c', where 'c' is the speed of the current, then the speed in still water is given by: \( b = \frac{(b + c) + (b - c)}{2} \)
2.
FLASHCARD QUESTION
Front
Define inverse variation in mathematics.
Back
Inverse variation occurs when one variable increases while the other decreases, such that their product is constant. If y varies inversely with x, then \( y = \frac{k}{x} \) for some constant k.
3.
FLASHCARD QUESTION
Front
How do you set up an equation for a round trip problem involving wind resistance?
Back
For a round trip against and with the wind, if the speed in still air is 's' and the wind speed is 'w', the time taken for the trip can be modeled as: \( \frac{d}{s - w} + \frac{d}{s + w} = t \), where d is the distance and t is the total time.
4.
FLASHCARD QUESTION
Front
What is an extraneous solution in the context of solving equations?
Back
An extraneous solution is a solution that emerges from the process of solving an equation but does not satisfy the original equation.
5.
FLASHCARD QUESTION
Front
If y varies inversely to x and y is 80 when x is 50, what is the constant of variation?
Back
The constant of variation k can be found using the formula: \( k = y \cdot x = 80 \cdot 50 = 4000 \).
6.
FLASHCARD QUESTION
Front
What is the relationship between distance, rate, and time?
Back
The relationship is given by the formula: \( d = r \cdot t \), where d is distance, r is rate (speed), and t is time.
7.
FLASHCARD QUESTION
Front
How do you solve for x in a rational equation?
Back
To solve for x in a rational equation, find a common denominator, eliminate the denominators by multiplying through, and then solve the resulting polynomial equation.
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