Problem Solving

U and V can complete a job together in 30 hours, V and W can do it in 40 hours, and W and U can do it in 60 hours. In how many hours will W finish the work individually?
A) 90hrs
B) 120 hrs
C) 240 hrs
D) 180 hrs
E) None of these\

OA isC...can some 1 plz post approach

So i post the straiightforward way but i am sure that there exists a better way.

(1) 1/u+1/v=1/30
(2) 1/v+1/w=1/40
(3) 1/w+1/u=1/60

These are the math translations.

So now you have to elimate variables.
For example: Subtract the second and third term from the first.

+ 1/u +1/v = 1/30
- 1/u -1/w = 1/60
= 0 +1/v -1/w =+1/60
- 0 -1/v -1/w = -1/40
= 0 0 -2/w = -2/240


1/w=1/240
240=w

mitaliisrani wrote:U and V can complete a job together in 30 hours, V and W can do it in 40 hours, and W and U can do it in 60 hours. In how many hours will W finish the work individually?
A) 90hrs
B) 120 hrs
C) 240 hrs
D) 180 hrs
E) None of these\

OA isC...can some 1 plz post approach

Another approach would be to plug in our own value for the job and then to plug in the answer choices, which represent the time for W to complete the job alone.

Job = 240.

Answer choice C:
Rate for W alone = work/time = 240/240 = 1/hr.
Rate for V+W together = work/time = 240/40 = 6/hr.
So rate for V alone = (V+W together) - (W alone) = 6-1 = 5/hr.
Rate for U+V together = work/time = 240/30 = 8/hr.
So rate for U alone = (U+V together) - (V alone) = 8-5 = 3/hr.
Rate for W+U together = work/time = 240/60 = 4/hr.
This works, because rate for W=1 and U=3, and 1+3 = 4/hr.

The correct answer is C.

just curious the source of this question. very complicated work problem and ive been having trouble with these....

just curious the source of this question. very complicated work problem and ive been having trouble with these....

mitaliisrani wrote:U and V can complete a job together in 30 hours, V and W can do it in 40 hours, and W and U can do it in 60 hours. In how many hours will W finish the work individually?
A) 90hrs
B) 120 hrs
C) 240 hrs
D) 180 hrs
E) None of these\

OA isC...can some 1 plz post approach

done
wow this PS is a bit time-consuming heheheh
1/u+1/v=1/30
1/v+1/w=1/40
1/w+1/u=1/60
we add em all together we will get
1/u+1/v+1/w=9/240
so 1/w =9/240-(1/u-1/v)=9/240-1/30=9/240-8/240=1/240
the answer is 240 C