Sabine and Hercule can assemble a table in 45 minutes. Working alone, it takes Hercule 48 minutes longer than Sabine to put this table together. How long would it take for Sabine to assemble the table by herself?
What formula would I use to solve this?
Don't look for "formulas", reason it out
Sabine's time = t hours
Hercules' time = t+48 minutes
combined time = 45 minutes
so job/t + job/(t+48) = job/45
notice I can divide by "job" and get
1/t + 1/(t+48) = 1/45
multiplying by 45t(t+48) I got
t^2 - 42t - 2160 = 0
solving this I got t = 72
You are really good. Thanks.
I really appreciate the breakdown of the problem.
To solve this problem, you can set up a system of equations. Let's represent the time it takes for Sabine to assemble the table by "x" minutes, and the time it takes for Hercule to assemble the table by "x + 48" minutes.
The equation for the combined time for both of them working together is:
1/x + 1/(x + 48) = 1/45
To solve this equation, you can apply the concept of least common denominator (LCD) to eliminate the denominators. Multiply both sides of the equation by the LCD, which is 45 * (x) * (x + 48). This will give you:
45 * (x) * (x + 48) * (1/x) + 45 * (x) * (x + 48) * (1/(x + 48)) = 45 * (x) * (x + 48) * (1/45)
Simplifying this equation will lead you to a quadratic equation. After solving the quadratic equation, you can find the value of "x," which represents the time it takes for Sabine to assemble the table by herself.
The quadratic equation can be solved using various methods, including factoring, completing the square, or using the quadratic formula.
Let me know if you would like me to solve the quadratic equation for you to find the value of x, or if there's anything else I can help you with!