Problem Solving

You can also approach this problem using the combined work equation: $$\frac{1}{A}+\frac{1}{B}=\frac{1}{A\ and\ B}$$ where the denominators on the left are how long it takes to get the job done alone vs. and the denominator on the right it how long it takes to get the job done together.

If Ali is 5 times faster than Moe, it should takes Moe 5 times as long to complete the job. Let's set the time it takes Ali to complete the job alone to x. This makes the time it takes Moe to complete the job alone 5x. We also know that it takes them 4 hours to complete the job together. Plugging all of this into the combined work equation gives $$\frac{1}{x}+\frac{1}{5x}=\frac{1}{4}$$ We want to solve for how long it would take Ali to complete the job alone, or x:$$\frac{5}{5x}+\frac{1}{5x}=\frac{1}{4}$$ $$\frac{6}{5x}=\frac{1}{4}$$ $$5x=24$$ $$x=\frac{24}{5}$$ $$x=4\frac{4}{5}$$
So it takes Ali 4 and 4/5 hours to complete the job. 4/5 of 60 minutes is 48 minutes, so it takes him 4 hours and 48 minutes.