Help!, Maths Question... SEC 2

---Max--- SG

A bathtub can be filled by Tap X alone in x min and by Tap Y alone in y min. If both taps are turned on at the same time, the bathtub can be filled in z min.

A. If both taps are turned on at the same time, what fraction of the bathtub is filled in one minute? Express your answer in x and y.

B. Find a formula connecting x, y and z.

C. Hence find the value of z when x = 20 and y = 12.

Neither do I understand the question nor do knew the steps to this question. I would really appreciate if any of the readers could give me to solution to the question or at least some hint on how I could solve this question.

Chapter 3.4 , Simple Algebraic Fraction, More About Formulae
Secondary 2, Singapore

skythewood SG

Fact: in one minute, tap X fills 1/x of the tub Fact: in one minute, tap Y fills 1/y of the tub

Forbiddensinner SG

B. Z ( X + Y ) = XY

C. Z ( 20 + 12 ) = 20x12

Z = 7.5

---Max--- SG

Err why the fact is 1/x or 1/y? Why is it 1 divide by x?

I don't understand whould anyone enlighten me?

syncopation_music SG

Err why the fact is 1/x or 1/y? Why is it 1 divide by x?

I don't understand whould anyone enlighten me?

tap x fill in x mins

if sharing the workload

x mins will become 1 / x bcos of the law of mathematics

tap y will share the workload thus become 1 /y

this is one of the uniqueness of algrebra

skythewood SG

Err why the fact is 1/x or 1/y? Why is it 1 divide by x?

I don't understand whould anyone enlighten me?

fact: Tap X fills the tub in x minutes.

===> Now, imagine x is 5. putting in real numbers will help you grasp the problem better

fact: Tap X fills the tub in 5 minutes.

in 1 minute, it fills 1/5 of tub.

====> Follow so far? it's the same if you imagine x to be 10, 15, or 20..

so in 1 minute, it fills 1/x of tub

---Max--- SG

Okay... Thank you skywood but could anyone guide me step by step on how do I solve question b and c? How did the formula came out? I seriously don't understand.

dkcx SG

b) you know that 1 min the tub is filled with 1/x + 1/y amount of water right?

So in z mins, the tank will be full so z X (1/x +1/y) = 1
multiply the equation by xy to remove denominator
zy + zx = xy
z (x+y) = xy

c) z (20 + 12) = 20 X 12
32z = 240
z = 7.5

vicodine SG

assume volume = v.

time to fill volume with tap x = x mins, so spd = v/x

time to fill volume with tap y = y mins, so spd = v/y

also given in qn: time to fill volume with both taps = z mins

so... i have speed and assumed volume for taps x and y.

form equation with the above...

v / (v/x +v/y) = z

v will cancel each other out.. leaving the answer : x y = z ( y + x )

subt in values to find c. Ans is 7.5

i think.. wrong dun blame me:p

skythewood SG

in one minute, Tap X fill 1/x of tub

in one minute, Tap Y fill 1/y of tub.

From question ==> if both tap turn on, tub will be filled in z minute.

======>I fill the tub in z minute using both tap, and get this equation

(1/x)*z + (1/y)*z = 1

=====> simplify

z(y +x)/xy = 1

z = xy/(x +y)

======> This is the simplest way i can explain it online. If you still can't grasp, i suggest you find your teacher.