AlgebraVery hardTime at which one candle is twice the height of another
Algebra practice question
Two candles of the same height are lit at the same time. One burns down completely in 4 hours and the other in 6 hours, each at a constant rate. After how many hours is the slower-burning candle twice the height of the faster one?
Answer: 3
With starting height 1, the heights after t hours are 1 − t/4 and 1 − t/6. Set 1 − t/6 = 2(1 − t/4): 1 − t/6 = 2 − t/2 → t/2 − t/6 = 1 → t/3 = 1 → t = 3.
Common wrong answers
- If you answered 2
- 2 is when the heights are 1/2 and 2/3, not in a 2 : 1 ratio.
- If you answered 4
- 4 is when the faster candle is gone.
- If you answered 1.5
- 1.5 halves the correct time.
More Algebra questions
- Very hard
For what value of c does the system 3x − 2y = 8 and 9x + cy = 5 have no solution? - Very hard
In the system 5x + 4y = 32 and 3x − 2y = 6, what is the value of 8x + 2y? - Very hard
The solution set of the inequality |ax − b| ≤ 6, where a and b are constants and a > 0, is 3 ≤ x ≤ 9. What is … - Very hard
The function f is linear, and for every value of x, f(x + 2) − f(x) = 6. If f(5) = 4, what is the value of f(0… - Very hard
In the system of equations 2x + 3y = 12 and 5x − 2y = k, where k is a constant, the solution (x, y) satisfies … - Very hard
In the xy-plane, the system of equations kx + 6y = 12 and 2x + (k − 1)y = 6, where k is a constant, has infini…
Not affiliated with the College Board. SAT is a trademark of the College Board.