GUYS PLEASE HELP!!!!

Joe can cut and split a cord of firewood in 3 fewer hours than Dwight can. When they work together, it takes them 2 hours. How

aalyn [17]

Answer:

Dwight will take 6 hours to finish the job alone and Joe will take 3 hours to finish the job alone.

Step-by-step explanation:

Let us assume the time taken by Dwight to split a cord of firewood = K hrs

So, the per hour rate of Dwight = $(\frac{1}{K})$

As, Joe uses 3 LESS hours then Dwight.

So, the time taken by Joe to split a cord of firewood = (K- 3) hrs

So, the per hour rate of Joe = $(\frac{1}{K-3})$

Now, when both of them wok together, it takes them 2 hours.

So, the per hour rate of BOTH of them = $(\frac{1}{2})$

⇒ Per hour rate of ( Dwight + Joe) = $(\frac{1}{2} )$

$\implies (\frac{1}{K}) + (\frac{1}{K-3}) = (\frac{1}{2})$

Now, solving for the value of K , we get:

$(\frac{1}{K}) + (\frac{1}{K-3}) = (\frac{1}{2})\\\implies \frac{(K-3) + K}{K (K-3)} = (\frac{1}{2})\\\implies 2(2K -3) = K^2 - 3K\\\implies k^2 - 3K -4K +6 = 0\\\implies K^2 - 7K + 6= 0\\\implies K^2 - 6K - K + 6= 0\\\implies K(K-6) -1(K - 6)= 0\\\implies (K-6)(K-1) = 0$

Implies either K = 6 Or K = 1

But if K = 1, (K-3) = 1- 3 = -2 hours would be A CONTRADICTION.

⇒ K = 6 hours

Hence, Dwight will take 6 hours to finish the job alone and Joe will take (k-3) = (6-3) = 3 hours to finish the job alone.

8 0

2 years ago

Robin purchased a piece of land in the year 2000 for $15,000. The value of the land increases at the rate of 13.17% each year. I

-Dominant- [34]

The value of the land increases by 13.17% each year So it's growth function which is V (t)=15000 (1+r)^t Where r is the growth rate which is in decimal 13.17/100=0.1317 So it's D) V(t) = 15000(1.1317)t; growth

6 0

2 years ago

What is thesimlified form of sqrt(48n^9)

garik1379 [7]

4n^4 √3n I believe would be the simplified form.

4 0

3 years ago

A certain car depreciates such that its value at the end of each year is p % less than its value at the end of the previous year

icang [17]

Answer:

b(b/a)^2

Step-by-step explanation:

Given that the value of the car depreciates such that its value at the end of each year is p % less than its value at the end of the previous year and that car was worth a dollars on December 31, 2010 and was worth b dollars on December 31, 2011, then

b = a - (p% × a) = a(1-p%)

b/a = 1 - p%

p% = 1 - b/a = (a-b)/a

Let the worth of the car on December 31, 2012 be c

then

c = b - (b × p%) = b(1-p%)

Let the worth of the car on December 31, 2013 be d

then

d = c - (c × p%)

d = c(1-p%)

d = b(1-p%)(1-p%)

d = b(1-p%)^2

d = b(1- (a-b)/a)^2

d = b((a-a+b)/a)^2

d = b(b/a)^2 = b^3/a^2

The car's worth on December 31, 2013 = b(b/a)^2 = b^3/a^2

4 0

3 years ago

Triangle inequality theorem-are the lengths 7, 4, and 2 of a triangle possible?

kakasveta [241]

You can't make a triangle with those lengths for sides.

The way I look at it is like this:

-- Take 2 sticks ... lengths 4 and 2 ... and connect them together at one end.

-- The farthest they can reach, if they're opened up completely and pointing
in opposite directions, is a distance of 6 .

-- They can't reach the ends of a stick that is 7 long. So you can't make
a triangle with those 3 sticks.

6 0

3 years ago