A rectangular mat has an area of 216 cm2. The width of the mat is 6 cm shorter than the length. Find the width of the mat.

Let $L$ be the length of the mat and $W$ be the width of the mat.

The area of the rectangular mat is $216 \text{ cm}^2$. The formula for the area of a rectangle is $A = L \times W$.

The width of the mat is $6 \text{ cm}$ shorter than the length.

We can factor the quadratic equation. We need two numbers that multiply to $-216$ and add to $-6$. These numbers are 12 and $-18$.

This gives two possible values for $L$:

Since length cannot be negative, we take $L = 18 \text{ cm}$.

Substitute $L = 18$ into equation (2):

The width of the mat is $\boxed{\text{12 cm}}$.

Let $M$ be the mother's present age and $D$ be the daughter's present age.

A mother is five times as old as her daughter.

Six years ago, their ages were $M-6$ and $D-6$. The product of their ages was 68.

Expand the equation:

Here, $a = 5$, $b = -36$, $c = -32$.

This gives two possible values for $D$:

Since age cannot be negative, the daughter's present age is $D = 8$ years.

Substitute $D = 8$ into equation (1):

The mother's present age is $\boxed{\text{40 years}}$ and the daughter's present age is $\boxed{\text{8 years}}$.