SOLUTION: A can do a piece of work in 2 days as B can do in 3 days. B can do as much work in 4 days as C can do in 5 days. If A,B& C finish the work together in 10 days. In how many days B c

Algebra ->  Rate-of-work-word-problems -> SOLUTION: A can do a piece of work in 2 days as B can do in 3 days. B can do as much work in 4 days as C can do in 5 days. If A,B& C finish the work together in 10 days. In how many days B c      Log On


   

Question 717612: A can do a piece of work in 2 days as B can do in 3 days. B can do as much work in 4 days as C can do in 5 days. If A,B& C finish the work together in 10 days. In how many days B can finish the work alone ?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A can do a piece of work in 2 days as B can do in 3 days.
2%2FA = 3%2FB
Cross multiply
3A = 2B
A = 2%2F3B
:
B can do as much work in 4 days as C can do in 5 days.
4%2FB = 5%2FC
4C = 5B
C = 5%2F4B
:
If A, B & C finish the work together in 10 days.
Let the completed job = 1
10%2FA + 10%2FB + 10%2FC = 1
Replace A and C
10%2F%28%282%2F3%29B%29 + 10%2FB + 10%2F%28%285%2F4%29B%29 = 1
Multiply by 10%2F12B, to clear the denominators
5%2F4(10) + 10%2F12(10) + 2%2F3(10) = 10%2F12B
50%2F4 + 100%2F12 + 20%2F3 = 10%2F12B
multiply by 12
3(50) + 100 + 4(20) = 10B
150 + 100 + 80
330 = 10B
B = 330/10
B = 33 days B can finish the work alone?