Final answer:
To calculate the time needed for 3 men to load 120 logs, we first determine the rate per man based on the original group of 5 men loading 90 logs in 15 minutes.
After calculating the combined rate of 3 men, we multiply by the number of logs to find the total time.
The correct answer is 33 minutes.
Step-by-step explanation:
The student is asking how long it would take for 3 men to load 120 logs onto a truck if 5 men can load 90 logs in 15 minutes. To solve this, we start by finding the rate at which the men can load the logs.
Together, the 5 men load 90 logs in 15 minutes, meaning one man loads 90/5 logs in 15 minutes, which is 18 logs. Therefore, one man can load 1 log in 15/18 minutes, simplified to 5/6 minutes per log.
Now, if 3 men are working together at the same rate, the combined rate would be 3 times the rate of one man. Since it takes 5/6 minutes per log for one man, it would take 3*(5/6) minutes to load 1 log by 3 men, which is 15/6 or 2.5 minutes per log.
For 120 logs, it would take 120 times 2.5 minutes, which totals 300 minutes. However, we want to find the time in minutes, so we divide 300 minutes by 60 to convert into hours and we get 5 hours. Since we are looking for an answer in minutes, 5 hours is equivalent to 5*60 = 300 minutes, which is not one of the answer options given, suggesting a need for re-evaluation of the calculation.
Upon re-evaluating, we realize that if one man loads a log in 5/6 minutes, then 3 men would load one log in (5/6)/3 or 5/18 minutes.
Therefore, they can load 120 logs in (5/18)*120 = 5*120/18. Simplifying this results in 5*120/18 = 5*6.6667, which is approximately 33.3333 minutes. So, the correct answer is 33 minutes, which matches option C of the multiple choices provided. Option C (33 minutes) is the correct answer.