- Let $x$ be the time (in hours) it takes Andy to do the job alone.
- Since Bob takes 3 fewer hours than Andy, Bob's time is $x - 3$ hours.
- Their combined work rate is the sum of their individual rates: $\frac{1}{x} + \frac{1}{x-3}$.
- Together, they complete the job in 2 hours, so their combined rate is $\frac{1}{2}$.
- This gives the equation: $\frac{1}{x} + \frac{1}{x-3} = \frac{1}{2}$.
- Solving this equation yields two solutions: $x = 6$ or $x = 1$.
- If $x = 1$, then Bob’s time would be $1 - 3 = -2$ hours, which is impossible.
- Therefore, the only valid solution is $x = 6$.
- It will take Andy 6 hours to do the job alone.
Parent Tip: Review the logic above to help your child master the concept of rational equation word problems worksheet.
