Two men and a woman are entrusted with a task. The second man needs three hours more to cope with the job than the first man and the woman would need working together. The first man, working alone, would need as much time as the second man and the woman working together. The first man, working alone, would spend eight hours less than the double period of time the second man would spend working alone. How much time would the two men and the woman need to complete the task if they all worked together?
- 2 hours
- 3 hours
- 4 hours
- 5 hours
W m1 , m2, w are the work rate per hr of man1 , man2 , women
x hrs is the time taken both by man 2 and women to complete the work .
The second man needs three hours more to cope with the job than the first man and the woman would need working together
Wm2 ( x + 3hr) = ( Wm2 + Ww ) * x hrs ---(i)Wm2 x + 3Wm2 = Wm2 x + Ww x
Wm2= ( Ww x ) / 3
k hrs is the time taken both by man 2 and women & man 1 Alone to complete the work .
The first man, working alone, would need as much time as the second man and the woman working together.
Wm1 * k hrs = ( Wm2 )* k + Ww k ---(ii)Substitution of Wm2= ( Ww x ) / 3 in (ii)
Wm1 k = (Ww * x * k) / 3 + Ww k
y hrs is the time taken by man 2 to complete the task alone .
The first man, working alone, would spend eight hours less than the double period of time the second man would spend working alone.
Wm1 ( 2y - 8 hrs ) = Wm2 * y hrs ---(iii)First we need to find the work rate of all persons ...
Wm2 ( x + 3hr) = ( Wm2 + Ww ) * x hrs ---(i)
Wm1 k = ( Wm2 ) k + Ww k ---(ii)
Wm1 ( 2y - 8) = Wm2 * y ---(iii)