Final answer:
By finding the rate of production and using it to calculate the time to produce 16 motorcycles, the time needed is determined to be 24 hours.
Step-by-step explanation:
To solve the problem, we first determine the rate at which motorcycles are produced in the factory. This is done by dividing the total number of motorcycles produced by the total number of hours. In this case, the factory produces 6 motorcycles in 9 hours. To find the rate, we perform the following calculation:
Rate = Number of motorcycles / Number of hours
Rate = 6 motorcycles / 9 hours
Rate = 2/3 motorcycle per hour
Once we have the rate, we can calculate the time it would take to produce 16 motorcycles by dividing the desired number of motorcycles by the rate of production:
Time = Number of motorcycles / Rate
Time = 16 motorcycles / (2/3 motorcycle per hour)
Time = 16 * (3/2) hours
Time = 24 hours
Therefore, it would take 24 hours to produce 16 motorcycles at this rate, which corresponds to option C.