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15390..15419 , 15420..15449 , 15450..15479 , 15480..15509 , 15510..15539 , 15540..15569 , 15570..15599 , 15600..15629 , 15630..15659, >>NextComplex_Numbers/351895: what does constant mean? Salami and More Deli sells a 5 foot submarine sandwich for parties. It weighs 8 pounds. Assuming that the weight per foot is constant, what would be the length of a 12-pound sandwich?
1 solutions
Answer 251715 by ankor@dixie-net.com(15657)   on 2010-10-05 15:35:50 (Show Source):
You can put this solution on YOUR website!what does constant mean? Here, it just means each foot of sandwich weighs the same;
:
Salami and More Deli sells a 5 foot submarine sandwich for parties.
It weighs 8 pounds.
Assuming that the weight per foot is constant, what would be the length
of a 12-pound sandwich?
:
two ways to do this:
Find the weight of 1 foot of sandwich
 = 1.6 lb per ft
then
 = 7.5 ft (7 ft 6 inches)
Or
you can use a ratio equation, let x = the length of 12 lb sandwich
 = 
Cross multiply
8x = 5 * 12
8x = 60
x = 
x = 7.5 ft
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expressions/352000: marrianne figured out that her father's age is hee age plus five to the power of four, less 365, minus 22, all divided by six. if her father is 42, how old is marrianne?
1 solutions
Answer 251589 by ankor@dixie-net.com(15657) on 2010-10-05 09:55:21 (Show Source):
You can put this solution on YOUR website!marrianne figured out that her father's age is her age plus five to the power
of four, less 365, minus 22, all divided by six. if her father is 42,
how old is marrianne?
:
Let m = her age
:
Write what it says:
"father's age is her age plus five to the power of four, less 365, minus 22, all divided by six."
42 = 
which is
42 = 
42 = 
Multiply both sides by 6 and rearrange
m + 238 = 6(42)
m = 252 - 238
m = 14 yrs old is M's age
:
:
You can check solution, substitute 14 for m in the original equation and see if you get 42
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Travel_Word_Problems/351956: Mr. March's car has new 22" tires on it. If he's driving at a constant speed of 60 mph, how many rotations will each tire complete in 1 minute
1 solutions
Answer 251558 by ankor@dixie-net.com(15657) on 2010-10-05 08:17:03 (Show Source):
You can put this solution on YOUR website!car has new 22" tires on it.
If he's driving at a constant speed of 60 mph, how many rotations will each tire complete in 1 minute
:
Find the circumference of the tire
C = 
C = 69.115 inches
:
How many ft traveled in 1 min at 60 mph
 = 5280 ft
:
Find no. of rpm
 = 76.4 rpm
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Travel_Word_Problems/351783: A motorboat can travel upstream on a river at 12 mph and downstream at 20 mph. How far upstream can the boat travel if it leaves at 8:00 am and must return by noon?
1 solutions
Answer 251430 by ankor@dixie-net.com(15657) on 2010-10-04 19:38:46 (Show Source):
You can put this solution on YOUR website!A motorboat can travel upstream on a river at 12 mph and downstream at 20 mph.
How far upstream can the boat travel if it leaves at 8:00 am and must return by noon?
:
From the information given we know we have to complete the round trip in 4 hrs
:
Let d = one way distance
:
Write a time equation: time = dist/speed
:
Time up + time down = 4 hrs
 +  = 4
Clear the denominators multiply by 60
60* + 60* = 60(4)
Cancel the denominators and you have:
5d + 3d = 240
8d = 240
d = 
d = 30 miles up-stream to return at noon
:
:
Confirm this, find the times
 +  =
2.5 + 1.5 = 4hrs
:
That was pretty easy, right?
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Linear_Equations_And_Systems_Word_Problems/351659: A field can be ploughed in 16 days. If 18 more hectares of land is ploughed daily, the work will be finished in 10 days. Find the area of the field.
1 solutions
Answer 251426 by ankor@dixie-net.com(15657) on 2010-10-04 19:22:22 (Show Source):
You can put this solution on YOUR website!A field can be ploughed in 16 days.
If 18 more hectares of land is ploughed daily, the work will be finished in 10 days.
Find the area of the field.
:
Let x = no. of hectares ploughed per day originally
The size of the field would be 16x
:
Let (x+18) = no. of hectares per day to finish in 10day
the size of the field would be 10(x+18)
:
A simple equation
16x = 10(x+18)
16x = 10x + 180
16x - 10x = 180
6x = 180
x = 
x = 30 hectares ploughed per day originally
then
16 * 30 = 480 hectares is the size of the field
:
:
Confirm this when he ploughs 30 + 18 = 48 hectares per day
10 * 48 = 480 hectares also
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Rate-of-work-word-problems/351851: three people painting a wall takes 2.5 hours. how many hours does it take for five people to paint the wall?
1 solutions
Answer 251413 by ankor@dixie-net.com(15657) on 2010-10-04 18:30:51 (Show Source):
You can put this solution on YOUR website!three people painting a wall takes 2.5 hours.
how many hours does it take for five people to paint the wall?
:
We can use man-hrs here
:
3*2.5 = 7.5 man-hrs to complete the job
:
Let t = time for 5 to do it
:
5t = 7.5
t = 
t = 1.5 hrs for 5 to complete the job
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Sequences-and-series/351303: Solve: Find a number that is 96 greater than its opposite.
x=the number
-x=opposite
x=96+-x
Is this right so far?
What do I do next?
Thanks
1 solutions
Answer 251342 by ankor@dixie-net.com(15657) on 2010-10-04 15:33:20 (Show Source):
You can put this solution on YOUR website!Solve: Find a number that is 96 greater than its opposite.
x=the number
-x=opposite
x=96+-x
Is this right so far?
Yes, just continue
x + x = 96
2x = 96
x = 96/2
x = 48
:
:
Prove this
48 - (-48) =
48 + 48 = 96
|
Average/351330: I am trying to help my daughter with Algebra, but it's been SO long... Here are two questions. I think if she can get the hang of it, she will take off. She is super-smart!
Sergio sells a mixture of Virginia peanuts and Spanish peanuts for $3.40 per pound. To make the mixture, he uses Virginia peanuts that cost $3.50 per pound and Spanish peanuts that cost $3.00 per pound. He mixes 10 pounds at a time. How many pounds of Virginia peanuts does he use?
and,
A pineapple drink contains 15 percent pineapple juice. How much pure pineapple juice should be added to 8 quarts of the pineapple drink to obtain a mixture containing 50 percent juice?
If you just want to pick one, that is fine. Thanks SO much! My e-mail is NordicStrength@aol.com
1 solutions
Answer 251322 by ankor@dixie-net.com(15657) on 2010-10-04 14:47:44 (Show Source):
You can put this solution on YOUR website!Sergio sells a mixture of Virginia peanuts and Spanish peanuts for $3.40 per pound.
To make the mixture, he uses Virginia peanuts that cost $3.50 per pound and
Spanish peanuts that cost $3.00 per pound.
He mixes 10 pounds at a time.
How many pounds of Virginia peanuts does he use?
:
This is a typical mixture problem, this method can be used for most of them:
Let x = amt $3.50 nuts required (Virginia)
then
(10-x) = amt of $3 nuts required
:
3.5x + 3(10-x) = 3.4(10)
3.5x + 30 - 3x = 34
3.5x - 3x = 34 - 30
.5x = 4
x = 
x = 8 lb of Virginia nuts required
:
:
Confirm this (10 - 8 = 2 lb of Sp nuts)
3.5(8) + 3(2) = 3.4(10)
28 + 6 = 34
:
:
A pineapple drink contains 15 percent pineapple juice.
How much pure pineapple juice should be added to 8 quarts of the pineapple
drink to obtain a mixture containing 50 percent juice?
:
Let x = amt of pure p.a juice
The resulting amt = (x+8)
:
.15(8) + 1x = .5(x+8)
1.2 + x = .5x + 4
x - .5x = 4 - 1.2
.5x = 2.8
x = 
x = 5.6 qts of pure p.a. juice required
:
:
Check this
.15(8) + 5.6 = .5(13.6)
1.2 + 5.6 = 6.8; confirms our solution
|
Complex_Numbers/351316: 3+5i........5-5i 4-5i
------ and ---- + ----
9-2i........1+5i 1+5i
I have been able to solve these problems in the form of a + bi but when it comes to fractions and dividing I am lost. Please help! Thank you so much!
1 solutions
Answer 251263 by ankor@dixie-net.com(15657) on 2010-10-04 12:20:14 (Show Source):
You can put this solution on YOUR website!3+5i........5-5i 4-5i
------ and ---- + ----
9-2i........1+5i 1+5i
:
Multiply by the conjugate of the denominator over itself (same as mult by 1)
*  =  =  =  = 
which is
 + 
reduce the fractions
 +  = 
:
:
 + 
these have the same denominator so we can
 = 
Multiply by the conjugate of the denominator
*  =  =  =  = 
|
Travel_Word_Problems/351120: pls. help me solve this problem. thank you.
A passenger on the front train A observes that he passes the complete length of train B in 33 seconds when traveling in the same direction as B and in 3 seconds when traveling in the opposite direction. If B is 330 ft long, find the speed of the two trains.
1 solutions
Answer 251066 by ankor@dixie-net.com(15657) on 2010-10-03 18:27:01 (Show Source):
You can put this solution on YOUR website!A passenger on the front train A observes that he passes the complete length
of train B in 33 seconds when traveling in the same direction as B and in
3 seconds when traveling in the opposite direction.
If B is 330 ft long, find the speed of the two trains.
:
Let a = train A's speed, Let b = train B's speed
:
When traveling in the same direction, their relative speed is (a-b)
When traveling in opposite direction, their relative speed is (a+b)
:
We will be finding the speeds in ft/sec
:
Write two distance equations, dist = speed * time
33(a-b) = 330
33a - 33b = 330
simplify, divide by 33
a - b = 10
and
3(a+b) = 330
3a + 3b = 330
simplify, divide by 3
a + b = 110
:
Use elimination on these two equations
a - b = 10
a + b = 110
-----------------adding eliminates b, find a
2a = 120
a = 
a = 60 ft/sec; speed of Train A; (that's  = 40.9 mph
and
a + b = 110
60 + b = 110
b = 110 - 60
b = 50 ft/sec; speed of Train B: (that's  = 34.1 mph
|
Geometry_Word_Problems/351109: x represent the side length of a square .find a regular polygon with side length x whose perimeter is twice perimeter of the square. find a regular polygon with side length x whose perimeter is three times the length of the square
1 solutions
Answer 251026 by ankor@dixie-net.com(15657) on 2010-10-03 15:56:52 (Show Source):
You can put this solution on YOUR website!x represent side length of a square .find a regular polygon with side length x
whose perimeter is twice the perimeter of the square.
:
4x = perimeter of original square
then
8x = twice the perimeter
:
let y = side of polygon with twice the perimeter
2x + 2y = 8x
Simplify, divide by 2
x + y = 4x
y = 4x - x
y = 3x
therefore
2x + 2(3x) = 8x
Polygon with twice the perimeter: 3x by x
:
find a regular polygon with side length x whose perimeter is three times
the length of the square
this perimeter: 3(4x) = 12x
let y = side of polygon with three times the perimeter
2x + 2y = 12x
Simplify, divide by 2
x + y = 6x
y = 6x - x
y = 5x
therefore
2x + 2(5x) = 12x
Polygon with three times the perimeter: 5x by x
|
Geometry_Word_Problems/350858: x represent side length of a square .find a regular polygon with side length x whose perimeter is twice the perimeter of the square. find a regular polygon with side length x whose perimeter is three times the length of the square
1 solutions
Answer 251025 by ankor@dixie-net.com(15657) on 2010-10-03 15:54:27 (Show Source):
You can put this solution on YOUR website!x represent side length of a square .find a regular polygon with side length x
whose perimeter is twice the perimeter of the square.
:
4x = perimeter of original square
then
8x = twice the perimeter
:
let y = side of polygon with twice the perimeter
2x + 2y = 8x
Simplify, divide by 2
x + y = 4x
y = 4x - x
y = 3x
therefore
2x + 2(3x) = 8x
Polygon with twice the perimeter: 3x by x
:
find a regular polygon with side length x whose perimeter is three times
the length of the square
this perimeter: 3(4x) = 12x
let y = side of polygon with three times the perimeter
2x + 2y = 12x
Simplify, divide by 2
x + y = 6x
y = 6x - x
y = 5x
therefore
2x + 2(5x) = 12x
Polygon with three times the perimeter: 5x by x
|
Money_Word_Problems/350959: My professor gave the class this problem, "the problem of the day", which is optional to do. I would really like to know how to solve this problem, but dont know how to start it. I have a really hard time with word problems.
Albert goes into a store and says "Lend me as much money as I already have, and i will spend $20.00 in your store." The owner agrees, and Albert spends $20.00. Albert does the same thing at a second, third, and fourth store, with the owner agreeing each time. After this Albert has no money. What is the total debt to the four store owners?
a.)$48.50 b.)$57.75 c.)$61.25 d.)$69.75 e.)$75.00
1 solutions
Answer 250863 by ankor@dixie-net.com(15657) on 2010-10-02 17:38:14 (Show Source):
You can put this solution on YOUR website!Albert goes into a store and says "Lend me as much money as I already have,
and i will spend $20.00 in your store."
The owner agrees, and Albert spends $20.00.
Albert does the same thing at a second, third, and fourth store, with the
owner agreeing each time.
After this Albert has no money.
What is the total debt to the four store owners?
:
Determine how much money, that Albert started out with
x = initial amt
:
First store lends him $x,
2x - 20 = amt he has when enters the 2nd store
:
2nd store lends him (2x-20), he spends 20 therefore
when he leaves the 2nd store he has:
2(2x-20) - 20
4x - 40 - 20
4x - 60 = amt when enters the 3rd store
:
3rd store lends him (4x-60), he spends 20 therfore
2(4x-60) - 20
8x - 120 - 20
8x - 140 = amt when enters the 4th store
:
The 4th store lends him (8x-140), he spends 20, has nothing left, therefore
2(8x-140) - 20 = 0
16x - 280 - 20 = 0
16x - 300 = 0
16x = 300
x = 
x = $18.75 is Al's initial amt
:
Total up what each store lent him, using the loan expression for each store:
Store 1: (18.75)
Store 2: 2(18.75) - 20 = $17.50
Store 3: 4(18.75 - 60 = $15
Store 4: 8(18.75 - 140) = $10
:
total debt: 18.75 + 17.50 + 15 + 10 = $61.25
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Proportions/350887: If jim can run 100m in 13.4 sec. and bill can run 100m in 14.1 sec. How much head start would bill need to finish at the same time? I know ther answer, but need to write it out in an equation.
1 solutions
Answer 250847 by ankor@dixie-net.com(15657) on 2010-10-02 15:45:08 (Show Source):
You can put this solution on YOUR website!If jim can run 100m in 13.4 sec. and bill can run 100m in 14.1 sec.
How much head start would bill need to finish at the same time?
:
Let x = no. of meters head start required by Bill
:
Find Bill's rate in meter/sec
 = 7.0922 m/sec
:
Write a time equation; Time = dist/rate
:
 = 13.4
100 - x = 7.0922 * 13.4
100 - x = 95.0355
-x = 95.0355 - 100
-x = -4.9645
x ~ 5.0 meter head start
:
:
Prove that by finding the time for each runner, should be equal.
Bill's time to run 95 meters: 95/7.0922 = 13.395 ~ 13.4, same as Jim's time to run 100 m
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Money_Word_Problems/350705: if you have $19.75 and a total of 100 coins, how many dimes is there?
1 solutions
Answer 250700 by ankor@dixie-net.com(15657) on 2010-10-01 20:08:26 (Show Source):
You can put this solution on YOUR website!if you have $19.75 and a total of 100 coins, how many dimes is there?
:
This solution is based on the fact that you only have dimes and quarters
d = no. dimes
q = no. of quarters
:
The total coin equation
d + q = 100
q = (100-d)
:
The total value equation
.10d + .25q = 19.75
Replace q with (100-d)
.10d + .25(100-d) = 19.75
.10d + 25.00 - .25d = 19.75
.10d - .25d = 19.75 - 25.00
-.15d = -5.25
d = 
d = 35 dimes
:
:
to check this, 100 - 35 = 65 quarters
.10(35) + .25(65) =
3.50 + 16.25 = 19.75, confirms our solution of 35 dimes
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Quadratic_Equations/350711: write a quadratic equation in the variable x having the given numbers as solutions. Type the equation in standard form, ax^2+bx+c=0. The solutions are -5,2
1 solutions
Answer 250697 by ankor@dixie-net.com(15657) on 2010-10-01 19:54:23 (Show Source):
You can put this solution on YOUR website!write a quadratic equation in the variable x having the given numbers as solutions.
Type the equation in standard form, ax^2+bx+c=0.
The solutions are -5,2
;
The factors of the equation could be:
(x+5)(x-2) = 0
Foil
x^2 - 2x + 5x - 10 = 0
;
x^2 + 3x - 10 = 0; the standard form
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Geometry_Word_Problems/350648: A circular path has a diameter of 120 meters. a person average walking speed is 4 kilometers per hour about how many minutes will it take him to walk around the path 3 times ?
1 solutions
Answer 250670 by ankor@dixie-net.com(15657) on 2010-10-01 16:02:47 (Show Source):
You can put this solution on YOUR website!A circular path has a diameter of 120 meters.
a person average walking speed is 4 kilometers per hour
about how many minutes will it take him to walk around the path 3 times ?
:
Find how many meter/min at 4 km/hr
 = 66  meters/min
:
Find the distance in meters for 3 laps around the track
 = 1131 meters
:
Find how long to walk 1131 meters at 66 meters/min ( use 66.67 meters)
 = 16.96 ~ 17 minutes
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Travel_Word_Problems/350519: A man commutes to work a distance 35 miles and returns on the same route at the end of the day. His average rate on the return trip is 20 miles per hour faster than his average rate on the outgoing trip. write the total time, T, in hours, devoted to his out going and return trips as a function of his rate on the outgoing trip, x. Then find an interpret T(25)
1 solutions
Answer 250661 by ankor@dixie-net.com(15657) on 2010-10-01 15:29:28 (Show Source):
You can put this solution on YOUR website!A man commutes to work a distance 35 miles and returns on the same route at the end of the day.
His average rate on the return trip is 20 miles per hour faster than his average
rate on the outgoing trip.
write the total time, T, in hours, devoted to his out going and return trips as a
function of his rate on the outgoing trip, x.
:
x = speed on the outgoing trip
then
(x+20) = speed on the return trip
:
Write a time equation, time = dist/speed
:
T(x) =  + 
:
Then find an interpret T(25)
T(25) =  + 
T(25) = + 
T(25) = 1.4 + .78
T(25) = 2.18 hrs total driving time
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Rate-of-work-word-problems/350649: if it takes 4 men to mow 4 lawns in 4 hours then how many men does it take to mow 50 lawns in 50 hours?
1 solutions
Answer 250630 by ankor@dixie-net.com(15657) on 2010-10-01 14:11:36 (Show Source):
You can put this solution on YOUR website!if it takes 4 men to mow 4 lawns in 4 hours then how many men does it take to mow 50 lawns in 50 hours?
:
Find how many man-hours to mow 1 lawn:  4 man-hours to mow 1 lawn
:
then 50 lawns would require: 4 * 50 = 200 man-hrs to do the job
:
let m = no. of men required to do the job in 50 hrs
50m = 200
m = 200/50
m = 4 men to do the job in 50 hrs
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Human-and-algebraic-language/350637: Petunia Pig wades into m mud puddles every h hours. How many mud puddles (x)does she wade into q hours?
PLEASE HELP ME!! I don't know how to do this!!! Thanks!!
1 solutions
Answer 250626 by ankor@dixie-net.com(15657) on 2010-10-01 14:03:02 (Show Source):
You can put this solution on YOUR website!Petunia Pig wades into m mud puddles every h hours.
:
Find out how many mud puddles per hr, that would be  puddles per hr
:
How many mud puddles (x)does she wade into q hours?
:
we know she wades into puddles every hr, therefore
x = q*
or
x =  puddles in q hrs
:
:
Did this make some sense to you now?
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Mixture_Word_Problems/350292: An aircraft carrier made a trip to Guam and back. The trip there took three hours and the trip back took four hours. It averaged 6 km/h on the return trip. Find the average speed of the trip there.
1 solutions
Answer 250475 by ankor@dixie-net.com(15657) on 2010-09-30 18:50:17 (Show Source):
You can put this solution on YOUR website!
I assume you are the student who sent the "Carrier to Guam" problem,
the only way I can contact you is by editing this problem;
:
A submarine left Hawaii two hours before an aircraft carrier.
The vessels traveled in opposite directions.
The aircraft carrier traveled at 25 mph for nine hours.
After this time the vessels were 280 miles apart.
Find the submarine’s speed.
:
Let r = submarines speed
Since they travel in opposite directions, their speeds are additive
:
Since the sub left 2 hrs early, it traveled for 11 hrs while the carrier traveled 9 hrs
:
Write a distance equation; dist = r*t
:
Sub dist + Carrier dist = 280
11r + 9(25) = 280
11r + 225 = 280
11r = 280 - 225
11r = 55
r = 55/11
r = 5 mph is the speed of the sub
:
Check this in the distance equation
11*5 = 9*25 = 280
:
Let me know if you get this, please
:
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An aircraft carrier made a trip to Guam and back.
The trip there took three hours and the trip back took four hours.
It averaged 6 km/h on the return trip. Find the average speed of the trip there.
:
Let s = speed to Guam
:
Write a distance equation; dist = speed * time
:
Trip there = Tip back
3s = 6*4
3s = 24
s = 
s = 8 km/hr there
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Linear_Equations_And_Systems_Word_Problems/349945: The sum of the digits in a two-digit number is 8. When the digits are reversed, the new number is 18 less than the original number. Set up the equations you would need to solve this problem – do not solve it please.
1 solutions
Answer 250200 by ankor@dixie-net.com(15657) on 2010-09-30 07:54:44 (Show Source):
You can put this solution on YOUR website!Let x = the 10s digit, Let y = the units
then
10x + y = "the original number"
10y + x = the "new number"
:
Just write an equation for what it says:
:
The sum of the digits in a two-digit number is 8.
x + y = 8
:
When the digits are reversed, the new number is 18 less than the original number.
10y + x = 10x + y - 18
you can simplify, combine like terms
10y - y = 10x - x - 18
9y = 9x - 18
Divide by 9
y = x - 2
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Numbers_Word_Problems/349765: three divided by the difference of x and 7 minus 2 divided by x plus 7 equals 3 times the reciprocal of the difference of x squared and 49 what is x
1 solutions
Answer 250117 by ankor@dixie-net.com(15657) on 2010-09-29 21:48:53 (Show Source):
You can put this solution on YOUR website!three divided by the difference of x and 7 minus 2 divided by x plus 7 equals
3 times the reciprocal of the difference of x squared and 49
what is x
:
Assume the problem is:
 -  = 
:
x^2-49 is the difference of squares and can be factored
- = 
:
Multiply by (x-7)(x+7), clears the denominators and you have:
3(x+7) - 2(x-7) = 3
:
3x + 21 - 2x + 14 = 3
:
3x - 2x + 35 = 3
:
x = 3 - 35
:
x = -32
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Travel_Word_Problems/349731: Two railroad workers were working together in a 1.2 Km mountain tunnel when a signal light flashed indicating the approach of a train, which was traveling at 60 Km/hr. Walking east, one worker reached the east end of the tunnel in 6 minutes, as the train entered the tunnle. The other worker reached the west end of the tunnel in 6 minutes and was passed by the train .24 Km beyond the west end of the tunnel. At what rate did each worker walk?
1 solutions
Answer 250026 by ankor@dixie-net.com(15657) on 2010-09-29 17:45:29 (Show Source):
You can put this solution on YOUR website!Two railroad workers were working together in a 1.2 Km mountain tunnel when a
signal light flashed indicating the approach of a train, which was traveling at 60 Km/hr.
Walking east, one worker reached the east end of the tunnel in 6 minutes, as the
train entered the tunnel.
The other worker reached the west end of the tunnel in 6 minutes and was passed
by the train .24 Km beyond the west end of the tunnel.
At what rate did each worker walk?
:
Let w = the speed of the westbound worker
:
After 6 min the worker was at the west end of the tunnel, and the train was
entering the east end of the tunnel, therefore
train traveled 1.2 + .24 = 1.44 km while the worker traveled .24 km
A ratio equation
 = 
1.44w = 60 * .24
1.44w = 14.4
w = 
w = 10 km/hr (the worker was running for his life, not walking)
;
Find the traveling speed of the eastbound worker (e)
6 min = .1 hrs
Find the point in the tunnel they were originally.
:
In 6 min w covered a distance of 10 * .1 = 1 km to the west end.
therefore the other worker's (e) only had to walk 1.2 - 1 = .2 km
His speed:
e =  = 2 km/hr, he really was walking
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Linear_Equations_And_Systems_Word_Problems/349512: Bill leaves his house for Makayla's house, riding his bicycle at 8 miles per hour. At the same time, Mikayla leaves her house, heading for bill's house walking at 3 miles per hour. Considering they live 8.25 miles apart please write a linear system that shows at what time they would meet.
1 solutions
Answer 249973 by ankor@dixie-net.com(15657) on 2010-09-29 15:10:34 (Show Source):
You can put this solution on YOUR website!Bill leaves his house for Makayla's house, riding his bicycle at 8 miles per
hour. At the same time, Mikayla leaves her house, heading for bill's house
walking at 3 miles per hour.
Considering they live 8.25 miles apart please write a linear system that shows at what time they would meet.
:
Let t = time B bikes and time M walks
:
When they meet their total distance will = 8.25 miles
Write a distance equation; dist = speed * time
:
B's dist + M's dist = 8.25 mi
8t + 3t = 8.25
11t = 8.25
t = 
t = .75 hrs or .75(60) = 45 minutes for them to meet
;
:
Check by finding the actual dist each traveled
8(.75) = 6 mi
3(.75) = 2.25
-------------
total: 8.25 mi; confirms our solution of t = .75
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Linear-systems/349457: A passenger trains speed is 60me/h and a freight train's speed is 40mi/h. The passenger train traels the same distance in 1.5 h less time than the freight train. How long does each train take to make the trip?
1 solutions
Answer 249970 by ankor@dixie-net.com(15657) on 2010-09-29 14:55:56 (Show Source):
You can put this solution on YOUR website!A passenger trains speed is 60me/h and a freight train's speed is 40mi/h.
The passenger train travels the same distance in 1.5 h less time than the freight train.
How long does each train take to make the trip?
:
Let t = time for the freight
then
(t-1.5) = time for the pass train to go the same distance
:
Write a distance equation; dist = speed * time
:
Pass dist = freight dist
60(t-1.5) = 40t
60t - 90 = 40t
60t - 40t = 90
20t = 90
t = 
t = 4.5 hrs for the freight
then
4.5 - 1.5 = 3 hrs for the pass
:
:
Confirm solution by finding the distances
3 * 60 = 180 mi
4.5*40 = 180 mi
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Human-and-algebraic-language/349625: 3 sisters are each 2 years apart in age. The youngest sister is Emily, the middle sister is Samantha and the oldest sister is Lauren. Together their combined ages are 42. How old is each sister?
1 solutions
Answer 249887 by ankor@dixie-net.com(15657) on 2010-09-29 10:38:38 (Show Source):
You can put this solution on YOUR website!3 sisters are each 2 years apart in age.
The youngest sister is Emily, the middle sister is Samantha and the oldest sister is Lauren.
Together their combined ages are 42.
How old is each sister?
:
This is just a consecutive even number problem
:
Let x = the youngest, then (x+2) and (x+4) are the other two
:
x + (x+2) + (x+4) = 42
3x + 6 = 42
3x = 42 - 6
3x = 36
x = 
x = 12 yrs is the youngest
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Travel_Word_Problems/349393: Dave is 1/3 of the way across the bridge when the sound of a train whistle brought him back to reality. Looking back over his shoulder he saw a huge locomotive pulling tons of box cars directly at him at 45 miles per hour. Using all of his powers of mathematical thought and analysis, Dave immediately figured tht he could run directly ahead and get to the far end of the bridge at the exact same time as the train. But he also knew that he could run back toward the train and get to the rear of the bridge just as the train got there. How fast does dave run?
1 solutions
Answer 249878 by ankor@dixie-net.com(15657) on 2010-09-29 09:42:59 (Show Source):
You can put this solution on YOUR website!Dave is 1/3 of the way across the bridge when the sound of a train whistle brought him back to reality.
Looking back over his shoulder he saw a huge locomotive pulling tons of box cars directly at him at 45 miles per hour.
Using all of his powers of mathematical thought and analysis, Dave immediately figured tht he could run directly ahead and get to the far end of the bridge at the exact same time as the train.
But he also knew that he could run back toward the train and get to the rear of the bridge just as the train got there.
How fast does dave run?
:
We can use logic here, Dave runs away from the train, we know that he will
have run 1/3 of the bridge when the train enters the opposite end.
That leaves 1/3 remaining for him to run while the train covers the whole dist of the bridge>
Another words, Dave runs 1/3 while the train runs 3/3 so he is running 1/3 * 45
Dave runs 15 mph
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Polynomials-and-rational-expressions/348952: solve the following system of equations:
x + y + square root(xy) = 28
x^2 + y^2 + xy = 336
1 solutions
Answer 249741 by ankor@dixie-net.com(15657) on 2010-09-28 18:16:11 (Show Source):
You can put this solution on YOUR website!solve the following system of equations:
x + y +  = 28
x^2 + y^2 + xy = 336
:
Simplify the 1st equation to use for elimination
x + y = 
square both sides
 = 
subtract xy from both sides
 = 
 =
:
Use for elimination with 2nd equation
 =
---------------------------Subtraction eliminates everything on the left, we have:
divide both sides by 56, results:
square both sides
xy = 64
y = 
:
Substitute for y in the 1st equation
x + y + = 28
x + +  = 28
x's inside the radical cancel
x + +  = 28
x + + 8 = 28
x + = 28 - 8
x + = 20
multiply by x
x^2 + 64 = 20x
A quadratic equation
x^2 - 20x + 64 = 0
Factors to
(x-16)(x-4)
x = 16
x = 4
:
Find y:
When x=16: y = 64/16 = 4
When x=4: y = 64/4 = 16
:
:
Check solution in the 1st equation
16 + 4 +  = 28
20 +  = 28; confirms our solutions; x=16, y-4 and x=4, y=16
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