Greg is 1.7 times faster at cleaning windows than Owen. It takes 39 minutes for them to clean 100 windows together. Using a rational equation, calculate how long it would take Owen to clean 100 windows by himself. Round the answer to the nearest tenth. (1 point)

Answer 1

Let $x$ be the number of minutes it takes Owen to clean 100 windows by himself. Since Greg is 1.7 times faster than Owen, the time it takes Greg to clean 100 windows by himself would be $\frac{x}{1.7}$.

Now we need to express their rates of cleaning windows.

• Owen's rate of cleaning windows is $\frac{100}{x}$ windows per minute.
• Greg's rate of cleaning windows is $\frac{100}{\frac{x}{1.7}}=\frac{100\cdot 1.7}{x}=\frac{170}{x}$ windows per minute.

When they work together, their combined rate is:

$$\frac{100}{x}+\frac{170}{x}=\frac{100+170}{x}=\frac{270}{x}\text{ windows per minute.}$$

We know it takes them 39 minutes to clean 100 windows together, so we can express this as:

$$\frac{270}{x}\cdot 39=100.$$

Now, multiply both sides by $x$:

$$270\cdot 39=100x.$$

Now, calculate $270\cdot 39$:

$$270\cdot 39=10530.$$

So we have:

$$100x=10530.$$

Now, divide both sides by 100 to solve for $x$:

$$x=\frac{10530}{100}=105.3.$$

Thus, it would take Owen approximately 105.3 minutes to clean 100 windows by himself.

So the final answer, rounded to the nearest tenth, is:

$$\boxed{{\displaystyle 105.3}}.$$