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1 year ago

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To collect data on the signal strengths in a neighborhood, Tracy must drive from house to house and take readings. She has a gra

duate student, Dave, to assist her. Tracy figures it would take her 8 hours to complete the task working alone, and that it would take Dave 12 hours if he completed the task by himself.
How long will it take Tracy and Dave to complete the task together?

1 answer:

Allisa [31]1 year ago

6 0

Tracy and Dave together complete the task in $\frac{24}{5}$ hours

Given Tracy alone take 8 hours to complete work and dave alone take 12 hours to complete the work.

Let's say together they worked in x hours

⇒in 1 hour they worked $\frac{1}{x}$ th part of the work

Tracy herself worked 8 hours to complete the whole task

⇒ in 1 hour Tracy completes $\frac{1}{8}$ th part of the task

Dave himself worked 8 hours to complete the whole task

⇒ in 1 hour Dave completes $\frac{1}{12}$ th part of the task

By proportions

⇒ $\frac{1}{8}$ + $\frac{1}{12}$ = $\frac{1}{x}$ { using operation addition}

⇒ x= $\frac{24}{5}$

Therefore,Tracy and Dave together complete the task in $\frac{24}{5}$ hours

Learn more about hour here:

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Answer:

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Step-by-step explanation:

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3 years ago

Can someone solve -3 = x + 7 - 4?

Blababa [14]

Answer:

x= -6

v= 1

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Step-by-step explanation:

-3= x+7-4, combine like terms by subtracting seven from four

-3= x+3, subtract three from both sides

-6= x

8v-3+3v= 8, combine like terms by adding 8v and 3v

11v-3= 8, add three to both sides

11v= 11, divide both sides by 11

v=1

-v+3v=4, combine like terms by adding -v and -3v

2v= 4, divide both sides by 2

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3 years ago

Read 2 more answers

The cost for 15 cases of oranges is $75. What is the cost for 1 case? *

postnew [5]

Answer:Ok I This question can be solved using a system of equation, which requires translating the above word problem into something that can be algebraically

Let O=oranges and Let G=Grapefruit

5O +8G=235

3O + 2G=85

To solve, you must isolate one of the variables and then work from there. To do that multiply both sides of the bottom or second equation by four and then subtract the bottom equation from the top.

Which would look like this

5O +8G=235

12O + 8G= 340

Then subtract the bottom from the top to get this

-7O=-105

Solving for O we divide both sides by -7, and end up with O=15

Plugging that value back into one of our original equations to solve for G we get this

3(15) + 2G= 85

45 +2G=85

2G=40

G=20

So 1 case of each altogether would equal 15+20, or $35.

<h3>Hope this helps have a awesome night/day❤️✨</h3>

Step-by-step explanation:

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3 years ago

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Answer:

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3 years ago

Postal regulations specify that a parcel sent by priority mail may have a combined length and girth of no more than 126 in. Find

Zarrin [17]

Answer:

The package of maximum dimensions has:

Width and height = 21 in each , and length = 42 in

Step-by-step explanation:

A package of square cross section has a girth equal to the perimeter of the square ("4 x" if we consider "x" as the side of the square). This quantity, added to the package's length "L" has to be no more than 126 in.

The maximum allowed for priority mail is therefore: $4x+L=126 \,in$

At the same time, we want the volume of the package to be a maximum. The volume of this parcel is defined as the product of all three dimensions of the package:

$V=width\,*\,height\,*\,length\\V=x\,*\,x\,*\,L\\V=x^2\,L$

We can now use the first formula for the priority mail maximum dimensions, to write L in terms of "x" and replace it in the volume formula:

$4x+L=126 \,in\\L=126-4x$

So now the volume expression becomes:

$V=x^2\,(126-4x)=126x^2-4\,x^3$

If the student doesn't know calculus, a graphing tool can be used to find the maximum.

With calculus derivatives the maximum can be easily found:

We can request the derivative of the volume to satisfy the conditions for derivative = 0 and the function concave down to locate the function's "maximum".

$V'(x)=252\,x-12\,x^2\\0=252\,x-12\,x^2\\0=12\,x\,(21-x)$

This tells us that there are two solutions to the derivative equal zero:

$x=0\,\,and\,\,x=21$

The first solution is clearly a minimum since it would render a package of zero volume. the second solution ( $x=21$ ) is the one that corresponds to the maximum of the volume function.

Therefore, the dimensions of the package of largest volume are: width and height: 21 in each, and length L= 126 - 4*21 = 42 in

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3 years ago