Final answer:
To calculate the rates of work for A, B, and C, divide 1 by the number of minutes it takes each of them to complete the task. Then sum these rates to find their combined rate of work. Finally, determine how long it would take them to complete the task together by taking the reciprocal of the combined rate.
Step-by-step explanation:
To calculate the rate of work for each person, we need to figure out how much of the task each person can complete in one minute. Since person A can complete the task in 150 minutes, their work rate is 1/150 of the task per minute. Similarly, person B can complete the task in 145 minutes, making their work rate 1/145 of the task per minute, and person C can complete it in 180 minutes, so their work rate is 1/180 of the task per minute. If they all work together, their combined work rate is the sum of their individual rates.
The combined rate is:
- Rate of A: 1/150 task/minute
- Rate of B: 1/145 task/minute
- Rate of C: 1/180 task/minute
To find this, we add these rates together:
1/150 + 1/145 + 1/180 = (145\*180 + 150\*180 + 150\*145) / (150\*145\*180)
Then, to find out how long it would take them to complete the task working together, we take the reciprocal of this sum as the total work is one whole task.