Line segment $A D$ is divided into three segments by points $B$ and $C$, so that $A B: B C=1: 2$ and $B C: C D=6: 5$. The length of $A D$ is 56 units. What is the length of $A B$ ?

![](https://cdn.mathpix.com/cropped/2024_04_17_03a8986aaed00af3ee97g-1.jpg?height=87&width=762&top_left_y=2426&top_left_x=736)
Let $x$ the real number satisfying $B C=6 x$.

From $A B: B C=1: 2$ we get that $A B=3 x$.

From $B C: C D=6: 5$ we get that $C D=5 x$.

This means $A D=A B+B C+C D=3 x+6 x+5 x=14 x$.

We are given that $A D=56$, so $56=14 x$ or $x=4$.

Therefore, $A B=3 x=3(4)=12$.

ANSWER: 12