Time/work math problem?

A, B and C could complete the work 6+5+3=14 times over in 150 days, so they could do it once together in 150/14 = 10⁵∕₇ days.

A and C stop after 8⁵∕₇ days, leaving B with 2 days of his work, 12/5 days doing As remaining work, and 6/5 days doing Cs remaining work, so B has 5⅗ days work left to complete.

n = total number of days

(n-2)/25+n/30+(n-2)/50 = 1

6(n-2)+5n+3(n-2) = 150

6n-12+5n+3n-6 = 150

14n = 168

n = 12 days

A & C did 10 days each

B did 12 days

Answer 2 days

.

Rate of Work:

A = ( 1 job / 25 days ) = ( 1/25 jobs /day )

B = ( 1 job / 30 days ) = ( 1/30 jobs /day )

A = ( 1 job / 50 days ) = ( 1/50 jobs /day )

Total days spent on the job = t

A = ( t - 2 ) days

B = ( t ) days

C = ( t - 2 ) days

Number of jobs completed in t days = 1 job

( 1/25 jobs /day ) ( t - 2 ) days + ( 1/30 jobs /day ) ( t ) days + ( 1/50 jobs /day )( t - 2 ) days = 1 job

t = 12 days

━━━━━

B worked on the task alone for 2 days during which he completed 2/30 = 1/15 of the task. A, B, and C worked together for x days to complete 14/15 of the task.

Combined rate = r = 1/25 + 1/30 + 1/50

r = (30*50 + 25*50 + 25*30)/(25*30*50) = 35/375 = 7/75 jobs/day

(7/75)x= 14/15

x = (14/15)(75/7) = 2*5 = 10 days

A, B, and C worked together for 10 days and B worked alone for 2 days. From start to finish, it took 12 days to complete the task.

A completes 1/25 of the work each day

B completes 1/30 of the work each day

C completes 1/50 of the work each day

Together, they complete 1/25 + 1/30 + 1/50 of the work each day

1/25 + 1/30 + 1/50 =>

6/150 + 5/150 + 3/150 =>

14/150

It takes them 150/14 days to complete the work together

They worked together for x days and then B worked alone for 2 days

(14/150) * x + (1/30) * 2 = 1

(14/150) * x + 1/15 = 1

(14/150) * x = 14/15

x = (14/15) * (150/14)

x = 10

x + 2 =>

10 + 2 =>

12

The work is completed in 12 days.