问题1：A所花的时间比B所花的时间少10天。如果A和B一起可以在12天内完成工作，请找出B花费的时间来完成工作。
解决方案：
Let us assume that B takes ‘x’ days to complete a piece of work.
So, B’s 1 day work = 1/x
Now, A takes 10 days less than that of B to finish the same piece of work so,
i.e., (x –10) days
⇒ A’s 1 day work = 1/(x – 10)
If both A and B work together for 12 days, then
(A and B)’s 1 day’s work = 1/12
Given:
A’s 1 day of work + B’s 1 day of work = 1/(x – 10) + 1/x
⇒ 1 + 1 = 1
x x – 10 12
⇒ x – 10 + x = 1
x(x – 10) 12
⇒ 12(2x – 10) = x(x – 10)
⇒ 24x – 120 = x2 – 10x
⇒ x2 – 10x – 24x + 120 = 0
⇒ x2 – 34x + 120 = 0
⇒ x2 – 30x – 4x + 120 = 0
⇒ x(x – 30) – 4(x – 30) = 0
⇒ (x – 30)(x – 4) = 0
Now, either x – 30 = 0
⇒ x = 30
Or, x – 4 = 0 ⇒ x = 4
It’s clear that the value of x cannot be less than 10, so the value of x = 30 is chosen.
Hence, the time taken by B to finish the piece of work is 30 days.
问题2：如果两个管道同时函数，贮存器会在12小时内被填充。一根管子比另一根管子更快地充满了10个小时。第二根管道要充满多少个小时才能充满水库?
解决方案：
Let us assume that the faster pipe takes x hours to fill the reservoir.
So, the portion of reservoir filled by faster pipe in one hour = 1/x
Given:
The slower pipe takes 10 hours more than that of faster pipe to fill the reservoir that is (x + 10) hours
So, Portion of reservoir filled by slower pipe = 1/(x + 10)
Now, it’s given that if both the pipes function simultaneously, the same reservoir can be filled in 12 hours
Therefore, as we know the portion of the reservoir filled by both pipes in one hour = 1/12
Now,
Portion of reservoir filled by slower pipe in one hour + Portion of reservoir filled by faster pipe in one hour = 1/x + 1/(x + 10)
Thus, the portion of reservoir filled by both pipes = 1/12
Hence,
⇒ 1 + 1 = 1
x x + 10 12
⇒ 12(2x + 10) = x(x + 10)
⇒ x2 – 14x – 120 = 0
⇒ x2 – 20x + 6x – 120 = 0
⇒ x(x – 20) + 6(x – 20) = 0
⇒ (x – 20)(x + 6) = 0
Now, either x – 20 = 0 ⇒ x = 20
Or, x + 6 = 0 ⇒ x = – 6 (can be neglected)
Since the value of time cannot be negative.
Thus, the value of x is taken as 20 hours.
Therefore, the time taken by the slower pipe to fill the reservoir = x + 10 = 30 hours.