Example

Solving a Work Application: Laying a Concrete Slab

Apply the problem-solving strategy for work applications to find how long it takes an individual to lay a concrete slab alone. If Tracy can lay the slab in 33 hours alone, let tt be the number of hours it takes Jordan to lay it alone. In 11 hour, Tracy lays 13\frac{1}{3} of the slab, and Jordan lays 1t\frac{1}{t} of the slab. Since it takes them 22 hours working together, their combined hourly rate is 12\frac{1}{2} of the slab. The rational equation is: 13+1t=12\frac{1}{3} + \frac{1}{t} = \frac{1}{2} Multiply both sides by the least common denominator, 6t6t: 6t \left(\frac{1}{3} + \frac{1}{t} ight) = 6t \left(\frac{1}{2} ight) Distribute and simplify: 2t+6=3t2t + 6 = 3t Subtract 2t2t from both sides: t=6t = 6 It would take Jordan 66 hours to lay the slab alone.

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Updated 2026-05-01

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