X, Y and Z can complete a piece of work individually in 6 hours, 8 hours and 8 hours respectively. However,…
X, Y and Z can complete a piece of work individually in 6 hours, 8 hours and 8 hours respectively. However, only one person at a time can work in each hour and nobody can work for two consecutive hours. All are engaged to finish the work. What is the minimum amount of time that they will take to finish the work?
6 hours 15 minutes
6 hours 30 minutes
6 hours 45 minutes
7 hours
Solution
To minimise time, X (the most efficient) should be used every alternate hour, starting first: X, (Y or Z), X, (Y or Z), X, ... X completes 16.67% per hour and Y or Z completes 12.5% per hour. After X+Y+X+Y+X+Y the work done is $3X + 3Y = 50 + 37.5 = 87.5\%$ in 6 hours. The remaining 12.5% is X's turn: X does it in $12.5/16.67$ hours = 0.75 hours = 45 minutes. Total = 6 hours 45 minutes.