SOLUTION: this is the kind of problem that I am having trouble with: Two numbers differ by 6 and their reciprocals differ by 8/15. Find the numbers. I have been able to figure out 2 equa

Question 387968: this is the kind of problem that I am having trouble with:
Two numbers differ by 6 and their reciprocals differ by 8/15. Find the numbers.
I have been able to figure out 2 equations based on that information:
x - y = 6 and 1/x - 1/y = 8/15
are these equations accurate?
If not, what should they be, instead?
If so, what are the next steps that I should take?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
You have the right idea, but there's a slight problem.

If , then this means that . So the first equation implies that (ie 'x' is the bigger number)

However, recall that if , then . So the equation implies that 'x' is the smaller number, which is a contradiction.

So the second equation should be
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