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Question
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?
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Answer
Let the time taken by 2 men be t1,t2 and woman be t3.
According to the equation we can form equations like
t2-(t2+t3)=3 eq.1
t1=t2+t3 eq.2
If we substitute eq2 value in eq1 we get t2-t1=3 eq.3
Another equation according to question
t1=2t2-8 eq.4
Solve 3&4 eqs.
We get t1 =2 hrs
t2+t3=2 hrs
Take their lcm we get 2 units total work and their efficiency also (1+1) we get 2units /hr
So time taken when working all three together is 2/2=1 hour
