s = hours it takes the small pipe on its own.
L = hours it takes the large pipe on its own.
we know the small pipe can do it in 11 hours total, so s = 11, so, how much of the whole job has the small done in 1 hour only?
well, if it takes 11 hours to do the whole thing, in 1 hour it has done only 1/11 of the whole job.
we know both pipes working together can do it in 6 hours flat. So in 1 hour only, both of them have done only 1/6 of the whole thing.
in that 1 hour, how much has the large one done? well, it has only done 1/L of the job.
![\bf \stackrel{\textit{how much has it been done by both in 1 hour}}{\stackrel{\stackrel{small}{rate}}{\cfrac{1}{s}}+\stackrel{\stackrel{large}{rate}}{\cfrac{1}{L}}~~=~~\stackrel{job}{\cfrac{1}{6}}} \\\\\\ \cfrac{1}{11}+\cfrac{1}{L}=\cfrac{1}{6}\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{66L}}{6L+66=11L}\implies 66=5L \\\\\\ \cfrac{66}{5}=L\implies 13\frac{1}{5}=L\impliedby \textit{13 hours and 12 minutes}](https://tex.z-dn.net/?f=%20%5Cbf%20%5Cstackrel%7B%5Ctextit%7Bhow%20much%20has%20it%20been%20done%20by%20both%20in%201%20hour%7D%7D%7B%5Cstackrel%7B%5Cstackrel%7Bsmall%7D%7Brate%7D%7D%7B%5Ccfrac%7B1%7D%7Bs%7D%7D%2B%5Cstackrel%7B%5Cstackrel%7Blarge%7D%7Brate%7D%7D%7B%5Ccfrac%7B1%7D%7BL%7D%7D~~%3D~~%5Cstackrel%7Bjob%7D%7B%5Ccfrac%7B1%7D%7B6%7D%7D%7D%20%5C%5C%5C%5C%5C%5C%20%5Ccfrac%7B1%7D%7B11%7D%2B%5Ccfrac%7B1%7D%7BL%7D%3D%5Ccfrac%7B1%7D%7B6%7D%5Cimplies%20%5Cstackrel%7B%5Ctextit%7Bmultiplying%20both%20sides%20by%20%7D%5Cstackrel%7BLCD%7D%7B66L%7D%7D%7B6L%2B66%3D11L%7D%5Cimplies%2066%3D5L%20%5C%5C%5C%5C%5C%5C%20%5Ccfrac%7B66%7D%7B5%7D%3DL%5Cimplies%2013%5Cfrac%7B1%7D%7B5%7D%3DL%5Cimpliedby%20%5Ctextit%7B13%20hours%20and%2012%20minutes%7D%20)
and you can round that up as needed.
Answer:
3 * 10^6 if the answer is 3.64 * 10^6, you really ought to argue the meaning of estimate with your instructor.
Step-by-step explanation:
This is a very valuable question. Put your calculator away when you answer it. Using a calculator is sort of cheating.
1.3 * 10^3 roughly is roughly 1 * 10^3
2.8*10^3 hours is roughly 3 * 10^3
Forget the powers for now and just work with the 1 and 3
1*3 equals 3.
10^3 * 10^3 = 10^6 when the base of two numbers is the same (10 in this case) then the powers are added.
10^(3 + 3) = 10^6
So the answer is roughly 3*10^6
Now you can take out your calculator and get the answer.
1.3*10^3 * 2.8 * 10^3 = 3.64 * 10 ^ 6
Notice that the estimate (done in my head) is close enough to tell you what the answer should be. On a test, that's a very handy skill.
−6.5(n−5)=18.2
distribute
-6.5n +32.5 = 18.2
subtract 32.5 from each side
-6.5n = -13.4
divide each side by -6.5
n=2.2
Answer n=2.2
Answer:
67.307
Step-by-step explanation:
30×25=750
100×80=8000
750+8000=8750
8750/130=67.307... total hits divided by total games
Answer:
colby
hourly rate =$8.90
overtime rate = time and a half = 1.5
the hourly overtime rate is the product of the overtime rate and the hourly rate.
hourly overtime rate= overtime rate × hourly rate
= 1.5 × $8.90
= $13.35
Cheryl
hourly rate = $7.10
overtime rate = double time = 2
the hourly overtime rate is the product of overtime rate and the hourly rate.
hourly overtime rate = overtime rate × hourly rate
= 2 × $7.10
= $14.20
<h3>Comparison</h3>
we note that the hourly overtime rate of cheryl is higher than the hourly overtime rate of colby, which implies that cheryl earns more for one hour of overtime.
we are also interested in the difference of the hourly overtime rate:
hourly overtime rate colby — hourly overtime rate cheryl
= $14.20 – $13.35
= $0.85
thus cheryl earns $0.85 more for one hour of overtime than colby .
<h3>result</h3>
<h2>cheryl,$0.85</h2>
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