Question

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Answer 1

The length of the shorter piece is
`5\textrm{ ft}`.

The length of the longer piece is
`11\textrm{ ft}`.

Explanation:

The five-step method is GUESS method.

Given:

Length of steel beam,
`L=16\textrm{ ft}`

Length of longer piece is 1 foot longer than twice the shorter one.

Unknown:

Length of longer and shorter pieces of beam.

Let the length of shorter piece be
`x` feet.

Therefore, the length of longer beam is equal to
`1+2x`

Evaluate:

Sum of lengths of longer and shorter pieces of beam is equal to the total length of beam. So,

`x+1+2x=16\\3x+1=16\\3x=16-1\\3x=15\\x=(15)/(3)=5`

Substitute and Solve:

Now, we have,
`x=5`.

Substitute 5 for
`x` for the lengths of shorter and longer pieces and solve for each. This gives,

Length of shorter piece =
`x=5\textrm{ ft}`

Length of longer piece =
`1+2x=1+2(5)=1+10=11\textrm{ ft}`

Therefore, the lengths of shorter and longer pieces are
`5\textrm{ ft}` and
`11\textrm{ ft}` respectively.