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)
Let Owen's speed of cleaning windows be x windows per minute.
Then Greg's speed of cleaning windows is 1.7x windows per minute.
Thus, Owen and Greg together can clean:
x + 1.7x = 2.7x windows per minute.
So 2.7x = 100 windows per 39 minutes.
Dividing both sides by 2.7, we get:
x = 100/2.7 windows per 39 minutes.
To find how long it would take Owen to clean 100 windows by himself, we can set up the equation:
100 = x * t,
where t is the time it takes for Owen to clean 100 windows.
Rearranging the equation, we get:
t = 100/x.
Substituting in the value of x that we found earlier, we get:
t = 100 / (100/2.7) = 2.7.
So it would take Owen approximately 2.7 minutes to clean 100 windows by himself.
Let's assume Owen's cleaning speed is represented by x windows per minute.
Since Greg is 1.7 times faster than Owen, Greg's cleaning speed can be represented as 1.7x windows per minute.
When they clean together, their total cleaning speed is x + 1.7x = 2.7x windows per minute.
We can set up a rational equation based on the given information:
100 / (2.7x) = 39
To solve for x, we can first multiply both sides of the equation by 2.7x:
100 = 39 * 2.7x
Divide both sides of the equation by 39 * 2.7:
100 / (39 * 2.7) = x
Simplifying the right side of the equation gives:
x ≈ 1.2
Therefore, it would take Owen approximately 1.2 minutes to clean 100 windows by himself.
To solve this problem using a rational equation, let's start by assigning variables to the unknowns. Let's denote the time Owen takes to clean 100 windows by himself as "x" (in minutes).
Now, based on the given information, we know that Greg is 1.7 times faster than Owen. This means that if Owen takes x minutes to clean 100 windows, Greg can do it in x/1.7 minutes.
Next, we're given that when they clean together, it takes them 39 minutes to clean 100 windows. To find how much work each does in one minute, we can set up the following equation:
1/x + 1/(x/1.7) = 1/39
The left side of the equation represents the work each person does in one minute. Adding their individual rates should equal the rate at which they work together, which is given as 1/39.
Now, let's simplify the equation:
1/x + 1/(x/1.7) = 1/39
To simplify the equation, we need to take the least common multiple (LCM) of the denominators, which is 1.7x:
1/x + 1/(x/1.7) = 1/39
1/x + 1.7/x = 1/39
Combining the fractions:
(1 + 1.7)/x = 1/39
Now, multiply both sides of the equation by x to isolate the term on the left side:
x * ((1 + 1.7)/x) = x * (1/39)
(1 + 1.7) = x/39
Add the numerators on the left side:
2.7 = x/39
To isolate x, we need to multiply both sides of the equation by 39:
2.7 * 39 = x
105.3 = x
So, Owen would take approximately 105.3 minutes to clean 100 windows by himself.
Rounding this to the nearest tenth gives an answer of approximately 105.3 minutes or 105.4 minutes.