A and B can do a piece of work in 10 hours, B and C in 12 hours and C and A in 15 hours. How long will they take if they work together? How long will each take to complete the work independently?
Answers
they independently do the work is 5 hours I have 6 hours 7 and half hours
Answer:
All together = 8 hr,
C = 40 hrs
B = 17⅐ hrs
A = 24 hrs
Step-by-step explanation:
A and B's 1 hr work = ⅒ (A+B)
B and C's 1 hr work = 1/12 (B+C)
C and A's 1 hr work = 1/15 (C+A)
(A+B)+(B+C)+(C+A) = ⅒ + 1/12 + 1/15 = 2(A+B+C)
2(A+B+C) = 6+5+4/60 = 15/60 = ¼ hr
(A+B+C) = ¼ × ½ = ⅛ hr
Therefore, all together can do the work in = 1 ÷ ⅛ = 8 hrs
Now,
A's work = [ A+B+C] - [B+C] = ⅛ - 1/12 = 1/24
= 1 ÷ 1/24 = 24 hrs
B's work = [A+B+C] - [C+A] = ⅛ - 1/15 = 7/120
= 17⅐hrs
C's work = [A+B+C] - [A+B] = ⅛ - ⅒ = 1/40
= 1 ÷ 1/40 = 40 hrs
Ans = All together can do the work in = 8 hrs
A can do in 24 hrs
B can do in 17⅐hrs
C can do in 40 hrs
