just checking to see if i have this problem correct
Sammy can cut wood twice as fast as Joe. When they both work together, it takes them 4 hrs. how long would it take them to do the job alone?
4/x +4/x+2 = x^2+2
4x+4x+8= x^2+2
8x+8= x^2+2
x^2-6x-8=0
(x-4)(x+2)
x=4 x=-2 since i can't use a -2 i have to put in a 4
x+2=4+2=6
Sammy =6 hours
6x2=12
Joe = 12 hours
Thanks
Yes, you have correctly solved the problem. Here's a step-by-step breakdown of how you arrived at the solution:
1. Let's assume Joe takes x hours to complete the job alone. Since Sammy can cut wood twice as fast as Joe, Sammy takes half the time, which is x/2 hours to complete the job alone.
2. When they work together, they can complete the job in 4 hours, so the equation becomes: 1/x + 1/(x/2) = 1/4 (since they complete 1 job in 1 hour, the fractions represent their rates of work).
3. To add the fractions, we need a common denominator. The common denominator is 2x, so the equation becomes: 2/2x + 1/x = 1/4.
4. Simplifying the equation: 2/(2x) + 1/x = 1/4.
5. Combining the fractions: (2+2)/(2x) = 1/4.
6. Simplifying further: 4/(2x) = 1/4.
7. Cross-multiplying and solving for x, we get: 4x = 8.
8. Dividing both sides by 4, we get: x = 2.
9. Since we are looking for the time it takes for Sammy to complete the job alone, we substitute x = 2 into x/2. Sammy takes 2/2 = 1 hour to complete the job alone.
10. Joe takes twice as long as Sammy, so Joe takes 1 * 2 = 2 hours to complete the job alone.
Therefore, the final answer is that Sammy takes 1 hour and Joe takes 2 hours to complete the job alone.