Say h = hours spent. We know Rachel finishes the job in 5 hours, thus, she finishes $\frac{1}{5}$ of the job in one hour. We also know Carl finishes the job in 8 hours, thus, he finishes $\frac{1}{8}$ of the job in one hour. Working together, this would equal:

$\frac{1}{5}+\frac{1}{8}$

$\frac{8}{40}+\frac{5}{40}$

$\frac{13}{40}$

Now, this is the rate per hour. Thus, multiply this by h to get how much of the work is done in terms of hours spent, and set it to 1 to find how many hours it would take to finish 100% of the job.

$\frac{13}{40}h=1$

$h=\frac{40}{13}$

$h\approx 3.0769$

Thus, it will take them approximately 3.0769 hours, or approximately 3 hours 4.614 minutes to finish the job together.

5 0

3 years ago

Meg's pension plan is an annuity with a guaranteed return of 7% per year (compounded quarterly). She would like to retire with a

Likurg_2 [28]

Answer:

$985.92

Step-by-step explanation:

In order to solve this question, we are going to use two formulas.

Present Value of an Annuity

$PV=PMT\frac{1-(1+i)^{-n} }{i}$

To get the value of the pension of 10,000 per quarter for 10 years. And

Sinking funds Payments Formula

$PMT=FV\frac{i}{(1+i)^{n}-1}$

to get the Payment to be deposited each quarter during 26 years.

So for the first formula

n= number of periods = we need to know how many quarters in 10 years are. We know there are 4 quarters in a year, so 10 years multiplied by 4 is 40 quarters

n= 40

For i=interest rate= it is 7% compounded quarterly. There are 4 quarters so we divide by 4 and we get:

i=7%/4=1,75%

PMT= 10,000

$PV=10,000\frac{1-(1+0.0175)^{-40} }{0.0175}\\\\PV=$285,942.30$

and these 285,942.30 would be our future value in the sinking fund payment formula with:

n= 26 years *(4 quarters a year)= 104 quarters

i=1.75%

FV=$285,942.30

$PMT=FV\frac{i}{(1+i)^{n}-1}\\\\PMT=285,942.30\frac{0.0175}{(1+0.0175)^{104}-1}\\\\PMT=985.92$

And $985.92 would have to be deposited every quarter during 26 years to get a payment of $10,000 per quarter for 10 years.

3 0

3 years ago

At the beginning of the week, James has 8 quarts of milk. At the end of the week there are 4 1/2 cups of milk left.

Anarel [89]

Answer: 3.5

Step-by-step explanation: 3.5

7 0

3 years ago