Machine A and B can finish a task in 6/5 of an hour. A and C and finish in 2/3 of an hour and B and C can finish in 2 hours. How long does it take for all three together to finish?
oops..posted in DS by mistake..how do i delete this?
5-Day Free Trial
5-day free, full-access trial TTP
Available with Beat the GMAT members only code
MORE DETAILS
Rate of work
This topic has expert replies
-
cans
- Legendary Member
- Posts: 1309
- Joined: Mon Apr 04, 2011 5:34 am
- Location: India
- Thanked: 310 times
- Followed by:123 members
- GMAT Score:750
a&b = 6/5 hours
a&c = 2/3 hours
b&c = 2 hours
(A&b)&(a&c)&(b&c) can finish in 1/ ( 1/(6/5) + (1/(2/3) + 1/2 ) = 1/ ( 5/6 + 3/2 + 1/2)) = 6/17
thus a&b&c can do in 3/17 hours
a&c = 2/3 hours
b&c = 2 hours
(A&b)&(a&c)&(b&c) can finish in 1/ ( 1/(6/5) + (1/(2/3) + 1/2 ) = 1/ ( 5/6 + 3/2 + 1/2)) = 6/17
thus a&b&c can do in 3/17 hours
If my post helped you- let me know by pushing the thanks button 
Contact me about long distance tutoring!
[email protected]
Cans!!
Contact me about long distance tutoring!
[email protected]
Cans!!
-
sourabh33
- Master | Next Rank: 500 Posts
- Posts: 135
- Joined: Tue Mar 22, 2011 12:01 pm
- Thanked: 21 times
- Followed by:3 members
- GMAT Score:720
IMO 12/17
Let the total work be 30 units
1. A+B -> Time taken = 6/5 -> Rate of work = 30/6/5 = 25 units/hr
2. A+C -> Time taken = 2/3 -> Rate of work = 30/2/3 = 45 units/hr
3. B+C -> Time taken = 2 -> Rate of work = 30/2 = 15 units/hr
Adding rates of all three we get 2(A+B+C)= 85
Therefore Rate f a+b+c = 85/2
Now to find the time taken by a+b+c -> work/rate -> 30/85/2 -> 60/85 -> 12/17
Let the total work be 30 units
1. A+B -> Time taken = 6/5 -> Rate of work = 30/6/5 = 25 units/hr
2. A+C -> Time taken = 2/3 -> Rate of work = 30/2/3 = 45 units/hr
3. B+C -> Time taken = 2 -> Rate of work = 30/2 = 15 units/hr
Adding rates of all three we get 2(A+B+C)= 85
Therefore Rate f a+b+c = 85/2
Now to find the time taken by a+b+c -> work/rate -> 30/85/2 -> 60/85 -> 12/17
