奧數問題請幫忙.....

設徒弟每天的工作量為 x 項任務, 則師傅每天的工作量為2x項任務
2(x + 2x) = 3/5
6x = 3/5
x = 1/10
徒弟在師傅停工2天完成2(1/10) = 1/5 項任務
餘下任務所需時間 = (1 - 3/5 - 1/5) / (x + 2x) = (1/5) / (3/10) = 2/3天
所以, 整項任務所需的時間 = (2 + 2 + 2/3) 天 = 14/3 天

師徒合作了2天完成一項任務的3/5後, 師傅因事故停工2天, 後繼續與徒弟合作, 已知師徒工作效率之比為2:1 , 問一共用了多少天才能完成這項任務 ?

Let r be the rate of the master. Then, the rate of the student is r/2.
Let n be the number of days required to finish the task.

Then, (r + r/2) x 2 = 3/5n or 3r = 3/5 n or r = n/5. ---------------(1)
In addition, 2 + (r/2) x 2 + (r + r/2) (2/5n - 2) = n
=> 2 + r + (3r/2) (2/5 n - 2) = n
=> 2 + r + 3r(n/5 - 1) = n
=> 2 + n/5 + 3(n/5)(n/5 - 1) = n
=> 2 - 4n/5 + 3(n^2/25 - n/5) = 0
=> 2 - 7n/5 + 3n^2/25 = 0
=> 50 - 35n + 3n^2 = 0
=> (10 - n)(5 - 3n) = 0
=> n = 10 or n = 5/3 (rejected) since n > 4
Therefore, it requires 10 days to finish the task.

設徒弟每天的工作量為 x , 則師傅每天的工作量為2x
2(x + 2x) = 3/5
6x = 3/5
x = 1/10
徒弟在師傅停工2天完成了 =2(1/10) = 1/5
師徒合作平均工作一天的速度=(3/5) / 2 =3/10
餘下所需日數 = (1 - 3/5 - 1/5) / (3/10) =2/3天
所以共用了(2 + 2 + 2/3)=14/3 天完成這項任務