1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
NikAS [45]
3 years ago
14

Two large and 1 small pumps can fill a swimming pool in 4 hours. One large and 3 small pumps can also fill the same swimming poo

l in 4 hours. How many hours will it take 4 large and 4 small pumps to fill the swimming pool.(We assume that all large pumps are similar and all small pumps are also similar.)
if u get this right i will mark brainliest
Mathematics
1 answer:
kolezko [41]3 years ago
6 0

Let <em>x</em> and <em>y</em> be the unit rates at which one large pump and one small pump works, respectively.

Two large/one small operate at a unit rate of

(1 pool)/(4 hours) = 0.25 pool/hour

so that

2<em>x</em> + <em>y</em> = 0.25

One large/three small operate at the same rate,

(1 pool)/(4 hours) = 0.25 pool/hour

<em>x</em> + 3<em>y</em> = 0.25

Solve for <em>x</em> and <em>y</em>. We have

<em>y</em> = 0.25 - 2<em>x</em>   ==>   <em>x</em> + 3 (0.25 - 2<em>x</em>) = 0.25

==>   <em>x</em> + 0.75 - 6<em>x</em> = 0.25

==>   5<em>x</em> = 0.5

==>   <em>x</em> = 0.1

==>   <em>y</em> = 0.25 - 2 (0.1) = 0.25 - 0.2 = 0.05

In other words, one large pump alone can fill a 1/10 of a pool in one hour, while one small pump alone can fill 1/20 of a pool in one hour.

Now, if you have four each of the large and small pumps, they will work at a rate of

4<em>x</em> + 4<em>y</em> = 4 (0.1) + 4 (0.05) = 0.6

meaning they can fill 3/5 of a pool in one hour. If it takes time <em>t</em> to fill one pool, we have

(3/5 pool/hour) (<em>t</em> hours) = 1 pool

==>   <em>t</em> = (1 pool) / (3/5 pool/hour) = 5/3 hours

So it would take 5/3 hours, or 100 minutes, for this arrangement of pumps to fill one pool.

You might be interested in
What is the length of line segment YX? 8 units 8 StartRoot 3 EndRoot units 12 units 12 StartRoot 3 EndRoot units.
timurjin [86]

Length of line segment <em>YX </em>is distance of both the ends of it. The length of line segment <em>YX </em>is 8\sqrt{3} units.

<h3>What is length of a line segment?</h3>

The length of a line segment is the measurement of the distance of both the ends of it.

Given information-

In the rectangle YVWX the length of line line segment YV is 24 units.

The rectangle YVWX is shown in the image below.

The angle given in the figure is,

m\angle X=30\\m\angle W=90\\m\angle V=60

Now in the figure of rectangle shown below, the triangle <em>XWV </em>is the right angle triangle.

In this right angle triangle the tan of angle is the ratio perpendicular to the base. thus,

\tan 60=\dfrac{24}{VW}\\\sqrt{3}=\dfrac{24}{VW}\\VW=8\sqrt{3}

As the opposite side of a rectangle are equal. Thus, the length of line segment is <em>VW </em>is equal to the length of the line segment <em>YX</em>. Therefore,

YX=VW=8\sqrt{3}

Hence, the length of line segment <em>YX </em>is 8\sqrt{3} units. The option B is the correct option.

Learn more about the line segment here;

brainly.com/question/2437195

3 0
2 years ago
Name the quadrant in which the point (−7, 3) lie
gtnhenbr [62]

Answer:

The quadrant in which the point (−7, 3) lie is the 2nd qudrant

4 0
2 years ago
Read 2 more answers
Karen wants to string lights around the edge of her deck. The shape and dimensions of her deck are shown in the diagram
Marianna [84]
She would need 70 feet of lights
8 0
2 years ago
What should i eat for breakfast?<br> A. eggs<br> B. human<br> C. bacon
Kisachek [45]

Answer:

C

Step-by-step explanation:

Because Bacon is good

4 0
3 years ago
Read 2 more answers
Which expressions show the prime factorization of 90?
Andreas93 [3]
Prime factorization means that we divide 90 by prime numbers only.

90 ÷ 2 = 45
45 ÷ 3 = 15
15 ÷ 3 =   5

2 x 3 x 3 x 5 = 90

2 x 3² x 5 = 90 
or 2,3,3,or 5

7 0
3 years ago
Other questions:
  • 70 Points!! Question!​
    7·2 answers
  • A class is raising funds to go ice skating at the rink at campus martius in detroit.The class plans to rent one bus. It costs $1
    15·1 answer
  • The local cell phone tower services for your provider
    9·1 answer
  • help on latest question? it's worth 100 pts and pretty easy im just lazy :) its also a math question :)
    12·2 answers
  • Code=oxi-vxsh-hrb join now for fun​ on plz join
    12·1 answer
  • What is an expression that is equivlant to 4x-7y-5z+6?
    6·1 answer
  • ASAP please i need helppp
    13·2 answers
  • Please I need help ASAP
    7·1 answer
  • Help this person please please please<br> https://brainly.com/question/21440589
    8·1 answer
  • Find the inverse function of f informally.<br> f(x) = x^3 + 8
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!