The man is 52 and his wife is 39.

The puzzle refers to the man as once being as old as the wife is “now.”  This gives you the first important piece of information; the man is older than the wife.  Second, you know that the two ages will add up to 91.  Third, you know that their difference in age is a constant variable.  You can’t, however, assume that they are close in age, but they must both be middle aged, otherwise it would be difficult to generate a number as high as 91 under the parameters of the problem.

So, after gathering this information, and some guess and check work, you’d find that the man is now twice the age (52) of her age (26) when he was the age she is now (39).

x years ago, her age was a0, his age was b0.
today, her age is a1, his age is b1.

the difference between their ages is constant.
1) b1-a1 = b0-a0

their ages combined today is 91
2) a1+b1 = 91

back then (x years ago) when his age was equal to her age now
3) b0 = a1

and his age now, is equal to twice her age back then (x years ago, when b0=a1)
4) b1 = 2a0

Now we have 4 variables, and 4 equations, we can solve for all variables by substitution.

To solve for b1,
2) a1=91-b1
3) b0 = a1 = 91-b1
4) a0 = b1/2

1) b1-(91-b1)= (91-b1)-b1/2
b1-91+b1 = 91-b1-(b1/2)
3.5*b1 = 2*91
b1 = 52

to solve for a1,
2) a1 = 91-52 = 39

since they are 13 years apart, a0 and b0 are 26 and 39 respectively.

m = man
w = woman
a = age difference

First we know their ages add up to 91:
m + w = 91

Second, we know there is an age difference of a:
m – a = w

Third, he is twice the age of her when he was her age now:
So when he was her age now, he was (m-a) which that means she was (w-a)
m = 2 * (w – a)

Now we have 3 equations and 3 variables.  Solve how you’d like.  Below is an example.
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Solving for m in terms of a:
m = 2 * ((m – a) – a)
m = 2 * (m – 2a)
m = 2m – 4a
m = 4a

Solving for w in terms of a:
4a – a = w
w = 3a

Solve for a:
4a = 91 – 3a
7a = 91
a = 13

Solve for m and w:
m = 4a
m = 4 * 13
m = 52

w = 3a
w = 3 * 13
w = 39