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
Joe's rate ---- 1/2x
Sammy's rate --- 1/x
combined rate = 1/x + 1/2x = 3/(2x)
time to do job with combined rate = 1/(3/(2x)) = 2x/3
but we know that is 4 hrs
2x/3 = 4
2x=12
x = 6 and then 2x = 12
So Sammy could do it 6 hours
and Joe would take 12 hours.
BTW, I won't even begin to point out all the errors in your solution.
Your opening equation makes no sense, and has no relation to the question.
the 2nd line does not follow from the 1st line
your "solution" of x=4 does not even satisfy your opening equation , as it should.
It looks like you knew what the answer was supposed to be, and simply formed some expression that contain that answer.
Yes, you have the problem correct!
To solve the problem, let's break it down step by step:
1. Let's assume that Joe takes x hours to complete the job alone. Since Sammy can cut wood twice as fast as Joe, it will take Sammy x/2 hours to complete the job alone.
2. When they work together, their work rates add up. So, their combined work rate is 1/x + 1/(x/2), which equals 4 hours.
3. To find a common denominator, we can simplify the equation as 2/(2x) + 1/(x/2) = 4.
4. Multiplying through by 2x will get rid of the fractions, so the equation becomes 4 + 4 = 8x.
5. Simplifying further, we have 8 = 8x, which means x = 1.
6. Now we know that it would take Joe 1 hour to complete the job alone. Since Sammy is twice as fast, it would take him 2 hours alone.
So, to answer the question, Joe would take 12 hours to complete the job alone, while Sammy would take 6 hours to complete the job alone.