Answer
The shorter piece is $2$ ft long
The longer piece is $8$ ft long
Work Step by Step
Step 1: The total length of the board is $10$ ft..
Step 2: We assume that the length of the shorter piece is $x$ ft..
Step 3: The length of the longer piece is therefore $4x$ ft..
Step 4: Since the shorter and longer piece together equal the total length of the board,
$x+4x=10$.
Step 5: Simplifying, $5x=10$
Step 6: $x=2$ ft
Step 7: Therefore, the shorter piece is $2$ ft long while the longer piece is $2\times4=8$ ft long.