GMAT Quantitative Reasoning Practice Test 1

Let $\mathit{x}=$ the part of the floor that can be tiled in 1 hour. Since Steve can tile a floor in 6 hours, he can tile $\frac{1}{6}$ of the floor in 1 hour. Since Cheryl can tile the same floor in 4 hours, she can tile $\frac{1}{4}$ of the floor in 1 hour. Use the equation $\frac{1}{6}+\frac{1}{4}=\frac{1}{\mathit{x}}$, where $\frac{1}{\mathit{x}}$ represents the part of the floor they can tile in an hour together. Multiply each term by the LCD $=12\mathit{x}.12\mathit{x}\times \frac{1}{6}+12\mathit{x}\times \frac{1}{4}=12\mathit{x}\times \frac{1}{\mathit{x}}$. The equation simplifies to $2\mathit{x}+3\mathit{x}=12.5\mathit{x}=12$. Divide each side by 5 to get $\mathit{x}=12∕5=2.4$ hours. Since 0.4 times 60 minutes equals 24 minutes, the final answer is 2 hours 24 minutes.