To solve this problem, we first need to determine the total amount of work done by the machines and then calculate how long it will take for fewer machines to complete the same amount of work.
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Calculate the total work done in machine-hours:
If 6 machines complete a task in 10 hours, the total work done is: \[ \text{Total Work} = \text{Number of Machines} \times \text{Time} = 6 \text{ machines} \times 10 \text{ hours} = 60 \text{ machine-hours} \] -
Determine how long it will take for 4 machines to complete the same work:
Let \( t \) be the time in hours it takes for 4 machines to complete the task. The amount of work done by 4 machines in \( t \) hours is: \[ \text{Work} = 4 \text{ machines} \times t \text{ hours} = 4t \text{ machine-hours} \]We know that 4 machines must accomplish the same total work of 60 machine-hours, so we set up the equation: \[ 4t = 60 \]
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Solve for \( t \): \[ t = \frac{60}{4} = 15 \text{ hours} \]
Therefore, it will take 4 machines 15 hours to complete the task.
The answer is: 15 hours.