A machine produces 280 pieces in 2.5 hours. To the nearest tenth of an hour, how long does it take to produce 640 pieces at this same rate?
Since the machine produces 280 pieces in 2.5 hours, its rate is $\frac{280}{2.5}=112\text{ pieces/hour}$. Setting this rate equal to $\frac{640}{x}$, we have $\frac{112}{1}=\frac{640}{x}$ or $\frac{640}{112}=x$. We have $x = \frac{80}{14} = 5\frac{20}{14} = 5\frac{10}{7}= \boxed{5.7}$ [to the nearest tenth of an hour].
To find out how long it takes to produce 640 pieces at the same rate, we can set up a proportion.
Let's call the time it takes to produce 640 pieces "x" hours.
We can set up the proportion:
280 pieces / 2.5 hours = 640 pieces / x hours
To solve for "x", we can cross-multiply and then solve for "x":
280 * x = 640 * 2.5
Simplifying the equation:
280x = 1600
Now, divide both sides of the equation by 280 to solve for "x":
x = 1600 / 280
x ≈ 5.71
Therefore, it takes approximately 5.71 hours (rounded to the nearest tenth) to produce 640 pieces at the same rate.
To find out how long it takes to produce 640 pieces at the same rate, we can set up a proportion:
280 pieces / 2.5 hours = 640 pieces / x hours
Cross-multiplying, we get:
280 * x = 640 * 2.5
Simplifying:
280x = 1600
Dividing both sides by 280:
x = 1600 / 280
x ≈ 5.7
To the nearest tenth of an hour, it would take approximately 5.7 hours to produce 640 pieces at the same rate.