greg is 1.7 times faster at cleaning windows than owen it takes 39 minutes for them to clean 100 windows together using rational equation calculate how long it would take only to clean 100 windows by himself round the answer to the nearest 10th

1 answer

Let's denote Owen's cleaning speed as \( r \) (in windows per minute). Since Greg is 1.7 times faster than Owen, his speed will be \( 1.7r \).

When Greg and Owen work together, their combined speed is:

\[ r + 1.7r = 2.7r \]

We know it takes them 39 minutes to clean 100 windows together.

The total work done (in windows) can be expressed as:

\[ \text{Work} = \text{Rate} \times \text{Time} \]

Thus, we can set up the equation:

\[ 100 = 2.7r \times 39 \]

Now we can solve for \( r \):

\[ 100 = 105.3r \] \[ r = \frac{100}{105.3} \approx 0.9496 \text{ windows per minute} \]

Now, we can find Greg's rate:

\[ 1.7r = 1.7 \times 0.9496 \approx 1.613 \text{ windows per minute} \]

Now we can find how long it would take for Owen alone to clean 100 windows. The time taken by Owen to clean 100 windows is given by:

\[ \text{Time} = \frac{\text{Work}}{\text{Rate}} = \frac{100}{r} \]

Substituting the value of \( r \):

\[ \text{Time} = \frac{100}{0.9496} \approx 105.3 \text{ minutes} \]

Thus, rounding to the nearest tenth, Owen would take approximately 105.3 minutes to clean 100 windows by himself.