# F.4 Maths Help !!測驗用 20 marks

Update:

117 ans : 30 hours

118 ans: 10 days

Rating

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.