Advanced MathVery hardNet rate as a single fraction
Advanced Math practice question
An inlet pipe fills a tank at a rate of 3/x tanks per hour, while a leak empties it at 1/(2x) tanks per hour, where x > 0. The net filling rate can be written as k/(2x) tanks per hour, where k is a constant. What is the value of k?
Answer: 5
3/x = 6/(2x), so the net rate is 6/(2x) − 1/(2x) = 5/(2x). Thus k = 5.
Common wrong answers
- If you answered 2
- 2 subtracts 3 − 1 without first converting 3/x to 6/(2x).
- If you answered 6
- 6 is the converted inlet rate's numerator, before subtracting the leak.
- If you answered 7
- 7 adds the rates instead of subtracting the leak.
More Advanced Math questions
- Very hard
The function f(x) = x² + 6x + 5 is rewritten in the form f(x) = (x + a)² + b. What is the value of b? - Very hard
What is the solution to the equation 6/(x − 2) = 3? - Very hard
The polynomial p(x) = x³ − 4x has how many distinct real zeros? - Very hard
The polynomial p is defined by p(x) = x³ + ax² + bx − 12, where a and b are constants. If x − 2 is a factor of… - Very hard
The function f, defined by f(x) = 3000(1.331)^(x/12), gives the value, in dollars, of an investment x months a… - Very hard
In the xy-plane, the parabola y = x² − 4x + 7 and the line y = mx − 2, where m is a constant, intersect at exa…
Not affiliated with the College Board. SAT is a trademark of the College Board.