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Darina [25.2K]
3 years ago
8

working together, two pumps can drain a certain pool in 4 hours. if it takes the older pump 9 hours to drain the pool by itself,

how long will it take the newer pump to drain the pool on its own?
Mathematics
2 answers:
Kryger [21]3 years ago
5 0
5 hours because u subtract 9 from 4 u get 5 hours
slava [35]3 years ago
3 0

Answer: Number of hours newer pump needed to drain is given by

7\dfrac{1}{5}\ hours

Step-by-step explanation:

Since we have given that

Number of hours taken by two pumps = 4 hours

Work done by two pumps = \dfrac{1}{4}

Number of hours taken by older pump = 9 hours

Work done by older pump = \dfrac{1}{9}

According to question, work done by new pump would be

\dfrac{1}{4}-\dfrac{1}{9}\\\\=\dfrac{9-4}{36}\\\\=\dfrac{5}{36}

So, Number of hours newer pump needed to drain is given by

\dfrac{36}{5}=7\dfrac{1}{5}\ hours

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Answer:

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You saved $300 to spend over the summer. You decide to budget $50 to spend each week.
Oduvanchick [21]

Answer:

<u>Part c) </u>

The Slope of the line is: m=-50 and represents the amount of money spent per week.

<u>Part d) </u>

The y-intercept is: c=300 and represents the maximum money we have that can be spend over the weeks (i.e. our maximum budget alowed).

Step-by-step explanation:

To solve this question we shall look at linear equations of the simplest form reading:

y = mx+c    Eqn(1).

where:

y: is our dependent variable that changes as a function of x

x: is our independent variable that 'controls' our equation of y

m: is the slope of the line

c: is our y-intercept assuming an x⇔y  relationship graph.

This means that as x changes so does y as a result.

<u>Given Information: </u>

Here we know that $300 is our Total budget and thus our maximum value (of money) we can spend, so with respect to Eqn (1) here:

c=300

The budget of $50 here denotes the slope of the line, thus how much money is spend per week, so with respect to Eqn (1) here:

m=50

So finally we have the following linear equation of:

y= - 50x + 300    Eqn(2).

Notice here our negative sign on the slope of the line. This is simply because as the weeks pass by, we spend money therefore our original total of $300 will be decreasing by $50 per week.

So with respect to Eqn(2), and different weeks thus various x values we have:

Week 1: x=1 we have y= -50 *1 + 300 = -50 +300 = 250 dollars.

Week 2: x=2 we have y= -50 *2 + 300 = -100 +300 = 200 dollars.

Thus having understood the above we can comment on the questions asked as follow:

<u>Part c) </u>

The Slope of the line is: m=-50 and represents the amount of money spent per week.

<u>Part d) </u>

The y-intercept is: c=300 and represents the maximum money we have that can be spend over the weeks (i.e. our maximum budget alowed).

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