Question

If a takes person A 11 minutes, person B 21 minutes, and person C 33 minutes to complete the same task individually, then how long would it take if they work together? Estimate your answer to two places after the decimal, if necessary.

Answer 1

Answer:

5.92 min

Step-by-step explanation:

1/11 = person A's rate

1/21 = person B's rate

1/33 = person C's rate

Let t = time working to gether

rt = am't  of work done

(1/11)t = work done by person A

(1/21)t = work done by person B

(1/33)t = work done by person C

(1/11)t + (1/21)t + (1/33)t = 1

231((1/11)t + 231(1/21)t + 231(1/33)t = 231

21t + 11t + 7t = 231

39t = 231

t = 5.92 min

I did that in super detail for you.  Note:  If n = the time to do a job alone, then 1/n = the rate of speed in doing the job.  And, the rate times the time on the job = am't  of work done.