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)
minutes
Let x be the amount of time it would take Owen to clean 100 windows by himself.
Therefore, Greg would take 1.7x amount of time to clean 100 windows by himself.
The total time it takes for them to clean 100 windows together is x + 1.7x = 2.7x.
Since the total time is 39 minutes, we can set up the equation 2.7x = 39.
Dividing both sides of the equation by 2.7, we get x = 14.4.
Therefore, it would take Owen approximately 14.4 minutes (rounded to the nearest tenth) to clean 100 windows by himself.
Let's assume that Owen takes x minutes to clean 100 windows by himself.
Since Owen is 1.7 times slower than Greg, Greg would take 1.7x minutes to clean 100 windows by himself.
When they work together, their combined rate is 1 + 1.7 = 2.7 times the rate of Owen working alone.
So, the equation can be set up as:
1 / x + 1 / 1.7x = 1 / 39
To solve for x, we can multiply all terms by 39 * (1.7x):
(39 * (1.7x) * 1 / x) + (39 * (1.7x) * 1 / 1.7x) = (39 * (1.7x) * 1 / 39)
Simplifying further:
(1.7) + 1 = 1.7x
2.7 = 1.7x
Dividing both sides by 1.7:
x = 2.7 / 1.7
x ≈ 1.59
Therefore, it would take Owen approximately 1.59 minutes to clean 100 windows by himself.
To solve this problem, we can set up a rational equation using the information given.
Let's say Owen's speed in cleaning windows is represented by x, which means Greg's speed is 1.7x (since Greg is 1.7 times faster).
Now, we can set up an equation based on the time it takes for them to clean 100 windows together.
The amount of time it takes for Owen to clean 100 windows is 100/x, and for Greg, it would be 100/(1.7x).
Since they work together, the sum of their individual rates is equal to their combined rate:
1/100 + 1/(1.7x) = 1/39
To solve this equation, we can multiply through by the least common multiple (LCM) of the denominators, which is 100 ⋅ 1.7x ⋅ 39.
(1/100) * 100 ⋅ 1.7x ⋅ 39 + (1/(1.7x)) * 100 ⋅ 1.7x ⋅ 39 = (1/39) * 100 ⋅ 1.7x ⋅ 39
Simplifying the equation, we get:
1.7x + 100 = 100 ⋅ 1.7x/39
Now, we can solve for x.
Multiply both sides by 39:
(1.7x + 100) ⋅ 39 = 100 ⋅ 1.7x
Distribute and simplify:
66.3x + 3900 = 170x
Subtract 66.3x from both sides:
103.7x = 3900
Divide both sides by 103.7:
x ≈ 37.60
So, Owen takes approximately 37.60 minutes to clean 100 windows by himself.