In a factory, 6 machines produce 180 units of a product in 2 hours. How long would it take for 10 machines to produce 600 units of the same product?
First, let's find the production rate of one machine:

Production_rate_per_machine = Units_produced_by_6_machines / (Number_of_machines * Time_taken)
                            = 180 / (6 * 2)
                            = 15 units per hour

Now, let's find the combined production rate of 10 machines:

Production_rate_10_machines = Production_rate_per_machine * Number_of_machines
                            = 15 * 10
                            = 150 units per hour

Finally, let's calculate how long it would take for 10 machines to produce 600 units:

Time_taken = Units_to_produce / Production_rate_10_machines
           = 600 / 150
           = 4 hours

So, it would take 10 machines 4 hours to produce 600 units of the product.