Henry Ernest Dudeney/Puzzles and Curious Problems/209 - A Running Puzzle

Puzzles and Curious Problems by Henry Ernest Dudeney: $209$

A Running Puzzle

$ABCD$ is a square field of $40$ acres.

The line $BE$ is a straight path, and $E$ is $110$ yards from $D$.

In a race Adams runs direct from $A$ to $D$,

but Brown has to start from $B$, go from $B$ to $E$, and thence to $D$.

Each keeps to a uniform speed throughout, and when Brown reaches $E$, Adams is $30$ yards ahead of him.

Who wins the race, and by how much?

Sources

• 1932: Henry Ernest Dudeney: Puzzles and Curious Problems ... (previous) ... (next): Geometrical Problems: Various Geometrical Puzzles: $209$. -- A Running Puzzle
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Geometrical Problems: Triangle, Square & Other Polygon Puzzles: $273$. A Running Puzzle