Workload 1
Algebra
Level
2
One man and two boys can do a piece of work in 12 days, which could be done in 6 days by three men and one boy. How many days would it take for one man to do it?
The answer is 20.
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1 solution
Let the rate of completing a piece of work W by one man be x . That is if it takes n days for a man to complete W , then we have n x = W . Similarly, let the rate of completing W by one boy be y . Then we have:
{ 1 2 ( x + 2 y ) = 1 2 x + 2 4 y = W 6 ( 3 x + y ) = 1 8 x + 6 y = W . . . ( 1 ) . . . ( 2 )
( 2 ) × 4 : 7 2 x + 2 4 y ( 2 a ) − ( 1 ) : 6 0 x ⟹ 2 0 x = 4 W = 3 W = W . . . ( 2 a )
Therefore, the number of days one man takes to complete the work is 2 0 .