Three workers working together need 1 hour to construct a wall. The first worker, working alone, can construct the wall twice as fast as the third worker, and can complete the task an hour sooner…
Question and options
Three workers working together need 1 hour to construct a wall. The first worker, working alone, can construct the wall twice as fast as the third worker, and can complete the task an hour sooner than the second worker. Then, the average of time taken in hours by three workers, when working alone, to construct the wall is
Answer and explanation
Correct answer: A - \(\dfrac{\sqrt{33} + 4}{3}\)
Let first take t h; third 2t, second t+1. 1/t+1/(t+1)+1/(2t)=1 gives 2t^2-3t-3=0, t=(3+sqrt(33))/4. Sum of times 4t+1=sqrt(33)+4, average (sqrt(33)+4)/3.
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