F.4 Maths Help !!測驗用 20 marks

117.
Let time taken by pipe B to fill the tank alone = x hrs.
time taken by pipe A to fill the tank alone = ( x - 10) hrs.
Part of the tank filled by pipe B in 1 hr. = 1/x
Part of the tank filled by pipe A in 1 hr. = 1/(x - 10)
Since the tank can be filled by A and B together in 12 hrs., so in 1 hr., 1/12 of the tank is filled. That is
1/x + 1/(x - 10) = 1/12
12(x - 10) + 12x = x(x - 10)
12x - 120 + 12x = x^2 - 10x
x^2 - 34x + 120 = 0
(x - 30)(x + 4) = 0
x = - 4 (rej.) or 30 hrs.
118.
Let time required by Stephy to complete the task alone = x days.
Time required by Miki to complete the task alone = (x + 5) days.
Time required for them to work together = (x - 4) days.
In 1 day, Stephy alone can complete 1/x of the work
In 1 day, Miki alone can complete 1/(x + 5) of the work.
In 1 day, working together can complete 1/(x - 4) of the work.
Therefore,
1/x + 1/(x + 5) = 1/(x - 4)
(x + 5)(x - 4) + x(x - 4) = x(x + 5)
x^2 + x - 20 + x^2 - 4x = x^2 + 5x
x^2 - 8x - 20 = 0
( x - 10)(x + 2) = 0
x = - 2 (rej.) or 10 days.