Question

Dominique can ice cupcakes twice as fast as houston. When they work together, dominique and houston can ice a large order of cupcakes in 5 hours. How many hours would it take houston to ice them by himself?

Answer 1

Answer: 15 hours

Step-by-step explanation:

Let Houston take x hours to ice them by himself.

⇒ Work done by him in one day when he works alone= $\frac{1}{x}$

Now, According to the question,

Dominique can ice cupcakes twice as fast as Houston.

⇒ Work done by him in one day when he works alone = $\frac{2}{x}$

Therefore, work done by Dominique and Houston in one day when they work simultaneously = $\frac{1}{x} + \frac{2}{x} = \frac{3}{x} = \frac{3}{x}$

But, When they work together, Dominique and Houston can ice a large order of cupcakes in 5 hours.

Therefore, their total work in one day when they work together = $\frac{1}{5}$

⇒ $\frac{1}{5} = \frac{3}{x}$

⇒ x = 15

Thus, Houston take 15 hours to ice them by himself.