Math Help - (1/(x+6))+(1/x)=(1/7)

Word Problem: Two companies working together can clear a parcel of land in 7 hours. Working alone, it would take Company A 6 hours longer to clear the land than it would Company B. How long would it take Company B to clear the parcel of land alone?

This is what I did:
Company A: x+6
Company B: x

Then it asked me to make an equation out of it. My answers we're all wrong, so I gave up and looked for the answer. And this is what they said:

** Can somebody explain to me why the numerators are 1s?

I got this far: x²-8x-42=0
Then, says I have to use the Quadratic Formula.
Tried to solve it but I always end up with a radical.. which is: (8±2√58)/2
and if simplified, would be (?): 4±√58
I re-checked several times but I cannot see what I did wrong..

I appreciate any help.

Thank You,
Azusa.

Think of the amount done in 1 hour Together they do 1/7th of the work. The fraction A alone would in 1 hour is 1/x and for B it would be 1/(x+6)

Hence together in 1 hour the fraction they would do would be 1/x+1/(x+6) which therefore =1/7

Thank you, but do you happen to know the answer to the 2nd part of my question?

For the 2nd part I can't see anything wrong with your working. Only the positive answer applies of course.

Originally Posted by biffboy

For the 2nd part I can't see anything wrong with your working. Only the positive answer applies of course.

Yep both +ve and -ve are correct ans for x - its just negative time doesn't make much sense to us.