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15390..15419 , 15420..15449 , 15450..15479 , 15480..15509 , 15510..15539 , 15540..15569 , 15570..15599 , 15600..15629 , 15630..15659, >>NextTravel_Word_Problems/466759: A relay race required runners to run from Point A to Point B and then back to point A. the distance from A to B = 22km.
On the return trip (Point B to Point A) the runners average speed decreased by (1.2km/hr).
If the relay took 10.5 hours to complete, what was the average speed from Point A to Point B.
Thank You
1 solutions
Answer 320051 by ankor@dixie-net.com(15649)   on 2011-07-03 13:56:28 (Show Source):
You can put this solution on YOUR website!A relay race required runners to run from Point A to Point B and then back to point A. the distance from A to B = 22km.
On the return trip (Point B to Point A) the runners average speed decreased by (1.2km/hr).
If the relay took 10.5 hours to complete, what was the average speed from Point A to Point B.
:
Let s = av speed from Point A to B
:
It says,"On the return trip (Point B to Point A) the runners average speed decreased by (1.2km/hr)." therefore:
(s-1.2) = return trip speed (B to A)
:
Write a time equation; time = dist/speed
 +  = 10.5
;
Multiply by s(s-1.2), results:
22(s-1.2) + 22s = 10.5s(s-1.2)
:
22s - 26.4 + 22s = 10.5s^2 - 12.6s
:
44s - 26.4 = 10.5s^2 - 12.6s
:
0 = 10.5s^2 - 12.6s - 44s + 26.4
:
A quadratic equation
10.5s^2 - 56.6s + 26.4 = 0
;
Multiply by 10 to get rid of the decimals
105s^2 - 566s + 264 = 0
:
Use the quadratic formula to solve this
a=105, b=-566, c=264, s=x
:
:
Two solutions, but only this one will make sense
s = 
s = 4.87 km/hr, av speed from A to B
:
:
Check this by finding the times
22/4.87 = 4.5 hrs
22/3.67 = 6.0 hrs
-----------------
tot time: 10.5 hrs, confirms our solution
|
Age_Word_Problems/466556: Please help.
The sum of the ages of Art, Ben, and Cal is 59. Art is 1 year older than Cal and Cal is 1 year younger than Ben. Which of these people were teenagers 7 years ago?
1 solutions
Answer 319949 by ankor@dixie-net.com(15649) on 2011-07-02 21:28:33 (Show Source):
You can put this solution on YOUR website!Write an equation for each statement:
;
The sum of the ages of Art, Ben, and Cal is 59.
a + b + c = 59
:
Art is 1 year older than Cal
a = (c+1)
:
and Cal is 1 year younger than Ben.
c = b - 1
or
b = (c+1)
Looks like a & b are the same age
:
Replace a and b in the 1st equation
(c+1) + (c+1) + c = 59
3c = 59 - 2
3c = 57
c = 
c = 19 yrs
then
a & b = 20 yrs
Which of these people were teenagers 7 years ago? All of them
|
Mixture_Word_Problems/466582: Hello,
I have a question I need help with. Your time is appreciated.
How many gallon of a 5% acid solution must be mixed with 30 gallons of 10% acid solution to obtain a mixture that is 8% acid?
Thank you
1 solutions
Answer 319945 by ankor@dixie-net.com(15649) on 2011-07-02 21:14:47 (Show Source):
You can put this solution on YOUR website!How many gallon of a 5% acid solution must be mixed with 30 gallons of 10% acid solution to obtain a mixture that is 8% acid?
:
Let x = amt of 5% acid required to accomplish this
:
Write the decimal equiv of the percent acid equation
:
.05x + .10(30) = .08(x+30)
.05x + 3 = .08x + 2.4
3 - 2.4 = .08x - .05x
.6 = .03x
x = 
x = 20 gal of 5% acid required
:
:
Check this
.05(20) + .10(30) = .08(20+30)
1 + 3 = .08(50)
4 = 4; confirms our solution
|
Evaluation_Word_Problems/466432: i seriously need some help with this problem! in 1993, the life expectancy of males in a certain country was 66.8 years. in 2000, it was 70.4 years. let E represent the life expectancy in year t and let t represent the number of years since 1993.
the linear function that fits the data is E(t) = ?t + ?
use the function to predict the life expectancy of males in 2003.
E(10) = ?
1 solutions
Answer 319925 by ankor@dixie-net.com(15649) on 2011-07-02 19:42:42 (Show Source):
You can put this solution on YOUR website!In 1993, the life expectancy of males in a certain country was 66.8 years.
in 2000, it was 70.4 years.
let E represent the life expectancy in year t and let t represent the number of years since 1993.
:
Find the slope
In 1993; x1=0 and y1=66.8
In 2000; x2=7 and y2=70.4
:
Find the slope (m) using the slope equation: m = 
m =  =  =
:
Use the point/slope formula to write the equation; y - y1 = m(x - x1)
y - 66.8 =  (x - 0)
y = x + 66.8
:
therefore:
The Linear function E(t) that fits the data is.
E(t)= t + 66.8
:
Use the Function to predict the life expectancy of males in 2003.
This means t=10; substitute 10 for t in the equation
E(10)= (10) + 66.8
E(10)= 5.1 + 66.8
E(10)~ 72 yrs is the life expectancy in 2003
|
Word_Problems_With_Coins/466563: Hello,
I have a question I need help answering. Your time is appreciated.
In Jose's coin jar there is a collection of nickels, dimes, and quarters which totals $4.05. There are twice as many quarters as nickels and 8 more dimes than nickels. How many coins of each kind are there?
1 solutions
Answer 319914 by ankor@dixie-net.com(15649) on 2011-07-02 18:46:31 (Show Source):
You can put this solution on YOUR website!coin jar there is a collection of nickels, dimes, and quarters which totals $4.05.
There are twice as many quarters as nickels and 8 more dimes than nickels.
How many coins of each kind are there?
:
Let n = no.of nickel
Let d = no. of dimes
let q = no. of quarters
:
Write an equation for each statement:
:
"coin jar there is a collection of nickels, dimes, and quarters which totals $4.05."
.05n + .10d + .25q = 4.05
:
"There are twice as many quarters as nickels"
q = 2n
:
"and 8 more dimes than nickels."
d = (n+8)
:
In the 1st equation, replace q with 2n, replace d with (n+8)
.05n + .10(n+8) + .25(2n) = 4.05
.05n + .10n + .8 + .50n = 4.05
.05n + .10n + .50n = 4.05 - 80
.65n = 3.25
n = 
n = 5 nickels
:
I'll let you find d and q, check solutions in the total$ equation.
|
Polynomials-and-rational-expressions/466394: Solve using the elimination method
1. -2x – 8y = 22 -6x – y = 20
2. x + 8y = 14 -3x + 4y = 0
3. 9x – 7y = -120.5 -36x + 28y = -482
Thank You So Much For Your Help!
1 solutions
Answer 319906 by ankor@dixie-net.com(15649) on 2011-07-02 18:10:25 (Show Source):
You can put this solution on YOUR website!Solve using the elimination method
1.
-2x – 8y = 22
-6x – y = 20
Multiply the 1st equation by -3:
+6x + 24y = -66
-6x - y = 20
------------------adding eliminates x find y
23y = -46
y = 
y = -2
Find x using the 1st equation
-2x - 8(-2) = 22
-2x + 16 = 22
-2x = 22 - 16
-2x = 6
x = 
x = -3
Check solutions in the 2nd equation
-6x - y = 20
-6(-3) - (-2) =
+18 + 2 = 20
:
:
2.
x + 8y = 14
-3x + 4y = 0
multiply the 1st equation by 3, do it the same way we did the 1st one
:
:
3.
9x – 7y = -120.5
-36x + 28y = -482
multiply the 1st equation by 4
+36x - 28y = -482
-36x + 28y = -482
these lines are parallel. No solution
|
Age_Word_Problems/466550: heather is twice as old as armida while kaye is 35 years youner than heather. if 1/2 the age ofarmida 5 years ago , and 1/3 of the age of heathr 10 years from now is twice the age of kaye, how old is kaye now?
1 solutions
Answer 319895 by ankor@dixie-net.com(15649) on 2011-07-02 16:24:40 (Show Source):
You can put this solution on YOUR website!Heather is twice as old as Armida while Kaye is 35 years younger than Heather.
If 1/2 the age of Armida 5 years ago, and 1/3 of the age of Heather 10 years from now, is twice the age of Kaye, how old is Kaye.
:
Let h = Heather's present age
Let a = Armida's
Let k = Kaye's
:
Write an equation for each statement:
:
"Heather is twice as old as Armida"
h = 2a
or
a = .5h
:
"while Kaye is 35 years younger than Heather."
k = h - 35
or
h = (k+35)
:
we need to get a in terms of k also
a = .5(k+35)
a = (.5k+17.5)
:
"If 1/2 the age of Armida 5 years ago, and 1/3 of the age of Heather 10 years from now, is twice the age of Kaye,"
 (a-5) +  (h+10) = 2k
:
multiply by 6 to clear the denominators, results:
3(a-5) + 2(h+10) = 6(2k)
3a - 15 + 2h + 20 = 12k
3a + 2h + 5 = 12k
replace h with 2a
3a + 2(2a) + 5 = 12k
3a + 4a + 5 = 12k
7a + 5 = 12k
Replace a with (.5k+17.5))
7(.5k+17.5) + 5 = 12k
3.5k + 122.5 + 5 = 12k
3.5k + 127.5 = 12k
127.5 = 12k - 3.5k
127.5 = 8.5k
k = 
k = 15 yrs is Kaye's age
:
:
A lot of chances to make a mistake here, check this:
h = 15 + 35 = 50
a = .5(50) = 25
Use these values in the statement:
"If 1/2 the age of Armida 5 years ago, and 1/3 of the age of Heather 10 years from now, is twice the age of Kaye,"
(25-5) + (50+10) = 2(15)
(20) + (60) = 30
10 + 20 = 30; confirms are solution
|
Linear_Equations_And_Systems_Word_Problems/466521: When Simon was born, his father was 36 years old. Five years ago, his father was twice as old as Simon will be in 7 years time. How old is Simon?
1 solutions
Answer 319890 by ankor@dixie-net.com(15649) on 2011-07-02 15:15:53 (Show Source):
You can put this solution on YOUR website!When Simon was born, his father was 36 years old.
Five years ago, his father was twice as old as Simon will be in 7 years time.
How old is Simon?
:
Let s = Simon's age
Let f = father's age
:
Write an equation for each statement:
:
"When Simon was born, his father was 36 years old."
f = s + 36
:
"Five years ago, his father was twice as old as Simon will be in 7 years time."
f - 5 = 2(s+7)
f - 5 = 2s + 14
f = 2s + 14 + 5
f = 2s + 19
Replace f with (s+36)
f + 36 = 2s + 19
36 - 19 = 2s - s
17 = s, Simon is 17 yrs old
:
:
Check solution in the statement (father is: 17 + 36 = 53 yrs old)
"Five years ago, his father was twice as old as Simon will be in 7 years time"
53 - 5 = 2(17 + 7)
48 = 2(24)
|
Age_Word_Problems/466517: A woman had seven children. On multiplying their ages together, one can obtain the number 6591. Given that today is the birthday of all seven children, how many triplets are there and what are all the seven ages?
1 solutions
Answer 319834 by ankor@dixie-net.com(15649) on 2011-07-02 08:10:17 (Show Source):
You can put this solution on YOUR website!A woman had seven children. On multiplying their ages together, one can obtain the number 6591. Given that today is the birthday of all seven children, how many triplets are there and what are all the seven ages?
:
Prime factor:
3 * 13 * 13 * 13 = 6591
:
How about two sets of triplets, ages 1, and ages 13, one child age 3?
for ages, 1 * 1 * 1 * 3 * 13 * 13 * 13 = 6591
|
Length-and-distance/466414: During the first part of a trip, a canoeist travels 59 miels at a certain speed. The canoeist travels 25 miles on the second part of the trio at a speed of 5 mph slower. The total time for the trip is 5 hrs. What was the speed of each part of the trip.
1 solutions
Answer 319786 by ankor@dixie-net.com(15649) on 2011-07-01 22:07:36 (Show Source):
You can put this solution on YOUR website!During the first part of a trip, a canoeist travels 59 miles at a certain speed.
The canoeist travels 25 miles on the second part of the trio at a speed of 5 mph slower.
The total time for the trip is 5 hrs. What was the speed of each part of the trip.
:
Let s = speed on the 1st part of the trip
then
(s-5) = speed on the 2nd part
:
Write a time equation; time = dist/speed
:
1st part time + 2nd part time = 5 hrs
 +  = 5
multiply by s(s-5), results;
59(s-5) + 25s = 5s(s-5)
:
59s - 295 + 25s = 5s^2 - 25s
:
84s - 295 = 5s^2 - 25s
:
Arrange as a quadratic equation on the right
0 = 5s^2 - 25s - 84s + 295
:
5s^2 - 109s + 295 = 0
:
use the quadratic formula to find s, only one solution will make sense
|
Rectangles/466398: I was doing an IQ game ("challenging" level) and was faced with a problem, which I solved by logical thinking and trial/error. However, before that I tried to figure out a way to solve the problem with algebra. I'm still not sure if it is possible or not.
The problem/question:
"Charlie removed a one-metre wide strip of grass from all the way around a square lawn, which was made info a flower bed. The remaining grass was four-fifths the area of the new flower bed.
What were the dimensions of the lawn originally?"
It seemed to me that we are missing a value (a length), but then I thought that it might be possible to figure it out by using equations, and canceling out values against each other. I tried different approaches, but I haven't done equations for a long time and got stuck.
This was my approach:
a = length or height of square lawn
b = new flower bed
c = remaining grass
d = dimensions of original lawn (area)
c = 4/5b
d = b + c
(a - 2)x2 = (4/5b) + (5/5b)
Is it just not possible, or am I missing something?
Any help with pointing out if and how this can be done would be greatly appreciated!
Kind regards,
Rob
1 solutions
Answer 319737 by ankor@dixie-net.com(15649) on 2011-07-01 18:47:24 (Show Source):
You can put this solution on YOUR website!Charlie removed a one-metre wide strip of grass from all the way around a square lawn, which was made into a flower bed.
The remaining grass was four-fifths the area of the new flower bed.
What were the dimensions of the lawn originally?
:
Let the original dimension of the square lawn = x by x
Area of original lawn = x^2
:
After removing the 1 meter strip all the way around, the dimensions would be:
(x-2) by (x-2)
Area of the remaining grass = (x-2)^2, FOIL this and you have:
A = x^2 - 4x + 4; the remaining grass
:
then find removed strip area:
A = x^2 - (x^2 - 4x + 4)
A = x^2 - x^2 + 4x - 4
A = 4x - 4, the area of the flowerbed
:
x^2 - 4x + 4 =  (4x - 4)
:
|
Quadratic_Equations/466249: Problem Solving: A sunflower plant was purchased with the following growth guarantee. After being planted, on the first day it would grow 100 mm. On the second day its height would increase by one half (50%), on the third day by one third, on the fourth day by one fourth, and so on. Assuming that the plant actually grows according to the guarantee, how many days would it take for it to reach its maximum height of 5000 mm?
1 solutions
Answer 319672 by ankor@dixie-net.com(15649) on 2011-07-01 12:02:43 (Show Source):
You can put this solution on YOUR website!A sunflower plant was purchased with the following growth guarantee.
After being planted, on the first day it would grow 100 mm.
On the second day its height would increase by one half (50%),
on the third day by one third, on the fourth day by one fourth, and so on
Assuming that the plant actually grows according to the guarantee, how many days would it take for it to reach its maximum height of 5000 mm?
:
Day 1: 100
Day 2: 100 + *100 = 150
Day 3: 150 + *150 = 200
Day 4: 200 +  *200 = 250
Day 5: 250 +  *250 = 300
Day 6: 300 +  *300 = 350
Day 7: 350 +  *350 = 400
From this we can see a pattern, that every day it will increase by 50:
50(d+1) = 5000
50d + 50 = 5000
50d = 5000 - 50
50d = 4950
d = 
d = 99 days to reach 5000 mm
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Numbers_Word_Problems/465912: If 1 more than a certain number is 3 less than a second number, the larger of these numbers minus he smaller is equal to
1 solutions
Answer 319645 by ankor@dixie-net.com(15649) on 2011-07-01 08:47:44 (Show Source):
You can put this solution on YOUR website!If 1 more than a certain number is 3 less than a second number, the larger of these numbers minus he smaller is equal to:
:
Let x = "a certain number"
Let y = "a second number"
:
x + 1 = y - 3
x = y - 3 - 1
x = y - 4
we can rewrite this to
y - x = 4
which answers the statement,"the larger of these numbers minus he smaller is equal to"
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Linear-systems/466169: Joe orders an 8 ounce martini that is 4.7% vermouth. sue orders an 8 ounce martini that is 100% gin. a martini is made with gin and vermouth. Joe and Sue give the drinks to Jane. Jane would like to mix a portion of each drink, so that she has an 8 ounce martini that is 99.8% gin. How much does Jane use of each drink?
1 solutions
Answer 319542 by ankor@dixie-net.com(15649) on 2011-06-30 21:27:24 (Show Source):
You can put this solution on YOUR website!Joe orders an 8 ounce martini that is 4.7% vermouth.
sue orders an 8 ounce martini that is 100% gin.
a martini is made with gin and vermouth.
Joe and Sue give the drinks to Jane.
Jane would like to mix a portion of each drink, so that she has an 8 ounce martini that is 99.8% gin.
How much does Jane use of each drink?
:
Let x = amt of Sue's drink which is pure gin
then
(8-x) = amt of Joe's drink which is 4.7% vermouth
Change Joes drink to per cent gin:
100 - 4.7 = 95.3% gin
:
Write a decimal equiv of per cent gin equation
Sues + Joes = Jane's
x + .953(8-x) = .998(8)
x + 7.624 - .953x = 7.984
x - .953x = 7.984 - 7.624
.047x = .36
x = 
x = 7.66 oz of pure gin from Sue's drink
then
8 - 7.66 = .34 oz of Joe's drink
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Surface-area/466166: hi, please help me with this word problem. The surface area of a cube is 864 square inches. Find the length of the lateral edge of the cube. thank youu
1 solutions
Answer 319540 by ankor@dixie-net.com(15649) on 2011-06-30 21:00:33 (Show Source):
You can put this solution on YOUR website!The surface area of a cube is 864 square inches.
Find the length of the lateral edge of the cube
:
The surface area of a cube = 6x^2
:
6x^2 = 864
x^2 = 
x^2 = 144
x = 
x = 12 inches
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Linear_Equations_And_Systems_Word_Problems/466060: The height of an object thrown upward from the floor of a canyon 106 ft. deep, with an initial velocity of 120 ft/sec is given by the equation:
h=-16t2 + 120t-106 How long will it take the object to rise to the height of the canyon wall? Round answer to the nearest hundreth.
1 solutions
Answer 319484 by ankor@dixie-net.com(15649) on 2011-06-30 16:00:01 (Show Source):
You can put this solution on YOUR website!The height of an object thrown upward from the floor of a canyon 106 ft. deep,
with an initial velocity of 120 ft/sec is given by the equation:
h=-16t2 + 120t-106 How long will it take the object to rise to the height of the canyon wall?
Round answer to the nearest hundreth.
:
Height of the canyon wall = 0, depth of the canyon -106, so we have
-16t^2 + 120t - 106 = 0
Use the quadratic formula:
In this equation: t=x, a=-16, b-120, c=-106
:
:
Two solutions
t = 
t = 1.023 sec, this is the solution we want, time at the top of the wall on the way up
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Miscellaneous_Word_Problems/466096: Please help me answer this question, thanks(:
The price per person of renting a bus varies inversely with the number of people renting the bus. It costs $20 per person if 56 people rent the bus. How much will it cost per person if 58 people rent the bus?
1 solutions
Answer 319447 by ankor@dixie-net.com(15649) on 2011-06-30 14:21:22 (Show Source):
You can put this solution on YOUR website!The price per person of renting a bus varies inversely with the number of people renting the bus.
It costs $20 per person if 56 people rent the bus.
How much will it cost per person if 58 people rent the bus?
:
You can use an inverse proportion equation, x = cost when 58 people rent it
 = 
58x = 20*56
x = 
x = $19.31
:
or
Find the original total cost of the bus
20 * 56 = $1120
:
find the cost per person when 58 people rent it
= $19.31
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Travel_Word_Problems/465940: how can i calculate average speed
when a plane is flying from one city to another and is 550 miles per hour and is 430 miles per hour on the return flight.
1 solutions
Answer 319431 by ankor@dixie-net.com(15649) on 2011-06-30 13:29:30 (Show Source):
You can put this solution on YOUR website!calculate average speed when a plane is flying from one city to another and
is 550 miles per hour and is 430 miles per hour on the return flight.
:
Let a = the average speed for the round trip
Let d = the one-way dist
:
Write a time equation: time = dist/speed
:
outbound time + return time = total time
 +  = 
Actually we don't need d, just put it in here to illustrate what we are doing here
Divide thru by d, and we have:
 +  = 
Multiply by 23650a to clear the denominators, results
43a + 55a = 47300
98a = 47300
a = 
a = 482.653 mph is the average speed
:
:
You can confirm this solution by choosing a value for d and finding the total of the actual times.
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Numbers_Word_Problems/465822: a five digit even number product of one's place and hundreds place is six and the sum is five tens place is greatest even number
1 solutions
Answer 319418 by ankor@dixie-net.com(15649) on 2011-06-30 12:33:51 (Show Source):
You can put this solution on YOUR website!The problem as I understand it:
:
A five digit even number:
The product of the one's place and hundreds place is six.
The sum is five times the tens place.
What is greatest even number?
:
Five digits, a, b, c, d, e
:
"The product of the one's place and hundreds place is six"
e * c = 6
Since the number is even, e = 2, therefore c = 3
:
"The sum is five times the tens place."
e + c = 5d
2 + 3 = 5d
5 = 5d
d = 1
:
The greatest even number: 99312
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Miscellaneous_Word_Problems/465868: One person can load a truck in 25 minutes, a second can load it in 50 minutes, and a third can load it in 10 minutes. how long will it take the three together to load the truck?
1 solutions
Answer 319261 by ankor@dixie-net.com(15649) on 2011-06-29 21:59:08 (Show Source):
You can put this solution on YOUR website!One person can load a truck in 25 minutes, a second can load it in 50 minutes,
and a third can load it in 10 minutes.
how long will it take the three together to load the truck?
:
Let t = time required if all three are loading
Let the completed job = 1; (a full truck)
:
Write a typical shared work equation
 +  +  = 1
multiply by 50, to clear the denominators, results:
2t + t + 5t = 50
8t = 50
t = 
t = 6.25 min working together
;
:
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Travel_Word_Problems/465817: A military helicopter traveled at 140 mph. A motorcycle traveled at 60 mph. The motorcycle traveled for three hours longer than the helicopter and went 100 miles farther than the helicopter. How far did the motorcycle travel? How many hours did the helicopter fly?
I know you are suppose to use the equation d=rt but I don't know how to set it up. I am not very good at word problems
Thanks
1 solutions
Answer 319226 by ankor@dixie-net.com(15649) on 2011-06-29 20:49:43 (Show Source):
You can put this solution on YOUR website!A military helicopter traveled at 140 mph.
A motorcycle traveled at 60 mph.
The motorcycle traveled for three hours longer than the helicopter and went 100 miles farther than the helicopter.
How far did the motorcycle travel?
:
Let d = dist traveled by the motorcycle
then
(d+100) = dist traveled by the helo
:
Write a time equation, time = dist/speed
Helo time + 3 hrs = Motorcycle time
 + 3 = 
multiply by 840 to clear denominators, results:
6(d+100) + 3(840) = 14d
6d + 600 + 2520 = 14d
3120 = 14d - 6d
3120 = 8d
d = 
d = 390 mi traveled by the motorcycle
:
:
How many hours did the helicopter fly?
390 + 100 = 490 mi traveled by the helo
 = 3.5 hrs
:
:
Check our solutions by finding the motorcycle time:
390/60 = 6.5 hrs which is 3 hrs more than the helo as was given
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Numbers_Word_Problems/465807: In the first 99 natural numbers, digit 4 comes how many times?
I got 4,14,24,34,40,41,42,43,44,45,46,47,48,49,54,64,74,84,94 (19 times)
But the answer written in my book is 20 times.
Which number am i missing?
1 solutions
Answer 319204 by ankor@dixie-net.com(15649) on 2011-06-29 18:52:47 (Show Source):
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Quadratic_Equations/465533: Solve the quadratic equation x2 - x = 30 by completing the square
1 solutions
Answer 319199 by ankor@dixie-net.com(15649) on 2011-06-29 18:38:20 (Show Source):
You can put this solution on YOUR website!Solve the quadratic equation x^2 - x = 30
:
x^2 - x + ___ = 30
Find the term that completes the square: half the coefficient of x, squared: (1/2)^2 = 1/4
Add to both sides
x^2 - x + = 30 +
x^2 - x + =  +
x^2 - x + = 
Which is:
(x - )^2 =
Find the square root of both sides
x - = +/- 
x - = +/- 
Two solutions
x = +
x = 
x = +6
and
x = -
x = 
x = -5
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Quadratic_Equations/465553: A river has a current of 5mph. It takes Al half an hour longer to paddle upstream 1.2 miles than to paddle downstream the same distance. What is Al's rate in still water.
Setting word problems up always seems to be more difficult than setting them up. I need to find a quadratic equation then solve with this problem.
1 solutions
Answer 319182 by ankor@dixie-net.com(15649) on 2011-06-29 17:24:43 (Show Source):
You can put this solution on YOUR website!A river has a current of 5mph. It takes Al half an hour longer to paddle upstream
1.2 miles than to paddle downstream the same distance.
What is Al's rate in still water.
:
Let s = his paddling rate in still water
then
(s+5) = his effective speed downstream
and
(s-5) = his effective speed upstream
:
Write a time equation, time = dist/speed
:
upstream time = downstream time + .5 hrs
 = 
:
multiply by (s-5)(s+5) to clear the denominators, results:
1.2(s+5) = 1.2(s-5) + .5(s+5)(s-5)
1.2s + 6 = 1.2s - 6 + .5(s^2 - 25)
:
Combine on the right
0 = 1.2s - 1.2s - 6 - 6 + .5s^2 - 12.5
:
Combine like terms, arrange as a quadratic equation
.5s^2 - 24.5 = 0
:
multiply by 2 to clear the decimals
s^2 - 49 = 0
s^2 = +49
s = 
s = 7 mph in still water
:
:
See if this is true, find the times
1.2/(7-5) = .6 hrs upstream
1.2/(7+5) = .1 hrs down
-------------------
time dif: = .5 hrs
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Miscellaneous_Word_Problems/465646: Suppose that at the end of any given year an automobile is worth only 80% of its value at the beginning of that year. If a car cost 17000 new what is its value at the end of five years?
At the end of five years the car is worth $
1 solutions
Answer 319179 by ankor@dixie-net.com(15649) on 2011-06-29 17:05:12 (Show Source):
You can put this solution on YOUR website!at the end of any given year an automobile is worth only 80% of its value at the beginning of that year.
If a car cost 17000 new what is its value at the end of five years?
At the end of five years the car is worth $
:
Use the decimal value of 80%
:
17000*.8^5 = $5,570.56 after 5 yeas
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Miscellaneous_Word_Problems/465752: A rain gutter is formed by bending up the sides of a 42-inch-wide rectangular metal sheet.
A) find a function that models the cross-sectional area of the gutter in terms of x.
Here is what I have so far, but don't know if it's on the right track:
A(x)=42-(1/3x)^2
1 solutions
Answer 319171 by ankor@dixie-net.com(15649) on 2011-06-29 16:09:12 (Show Source):
You can put this solution on YOUR website!A rain gutter is formed by bending up the sides of a 42-inch-wide rectangular metal sheet.
:
Let the cross section look like something like this, where x is the height and w is the width.
:
x|_w_|x
:
then
2x + w = 42
w = (42-2x)
:
A) find a function that models the cross-sectional area of the gutter in terms of x.
A = x * w
Replace w with (42-2x)
A(x) = x(42-2x)
A(x) = -2x^2 + 42x
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Rate-of-work-word-problems/465706: Tom can paint a room in 5 hours; if he works with Tim, they can paint together the same room in 2 hours. How long does it take for Tim to paint the room by himself?
I came up with 1/5 – 1/2 = x
I think X would be 3, that Tim could paint the room in 3 hours. But I am not sure. Please help any advice would be great, tahnk you!
1 solutions
Answer 319162 by ankor@dixie-net.com(15649) on 2011-06-29 15:59:02 (Show Source):
You can put this solution on YOUR website!Tom can paint a room in 5 hours; if he works with Tim, they can paint together the same room in 2 hours.
How long does it take for Tim to paint the room by himself?
:
Here is a simple and understandable method of doing these shared work problems
:
Let t = Tim's time working alone
Let the completed job = 1
:
Each man will do a fraction of the job; the two fractions must add up to 1 (a complete job)
:
 +  = 1
Multiply by 5t to clear the denominators, results
2t + 5(2) = 5t
2t + 10 = 5t
10 = 5t - 2t
10 = 3t
t = 
t = 3 hrs Tim working alone
:
:
See if these two fractions add up to 1
2/5 + 2/3.33
.4 + .6 = 1
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Percentage-and-ratio-word-problems/465528: How much 20% anti-freeze should be mixed with 60% anti-freeze to get 10 liters of 28% anti-freeze?
1 solutions
Answer 319152 by ankor@dixie-net.com(15649) on 2011-06-29 15:46:20 (Show Source):
You can put this solution on YOUR website!How much 20% anti-freeze should be mixed with 60% anti-freeze to get 10 liters of 28% anti-freeze?
:
Let x = amt of 60% stuff
then
(10-x) = amt of 20%
:
Write a mixture equation using decimals
.60x + .20(10-x) = .28(10)
.60x + 2 - .20x = 2.8
.6x - .2x = 2.8 - 2
.4x = .8
x = 
x = 2 liters of 60% stuff
then
10 - 2 = 8 liters of 20%
:
:
Check this: .6(2) + .2(8) = .28(10)
1.2 + 1.6 = 2.8
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Numbers_Word_Problems/465603: Find 4 consecutive odd integers where the product of the two smaller numbers less than the product of the two larger numbers.
1 solutions
Answer 319114 by ankor@dixie-net.com(15649) on 2011-06-29 14:34:59 (Show Source):
You can put this solution on YOUR website!Find 4 consecutive odd integers where the product of the two smaller numbers less than the product of the two larger numbers.
:
4 consecutive odd integers, x, (x+2), (x+4), (x+6)
:
where the product of the two smaller numbers less than the product of the two larger numbers.
x(x+2) < (x+4)(x+6)
FOIL
x^2 + 2x < x^2 + 6x + 4x + 24
x^2 + 2x < x^2 + 10x + 24
x^2 - x^2 + 2x - 10x < 24
-8x < 24
x has to be positive, multiply both sides by -1, this reverses the inequality sign
8x > -24
x > 
x > -3
An odd number greater than -3, is -1,
then the 4 odd integers: -1, +1, +3, +5
:
See if this satisfies the statement:
-1(+1) < 3 * 5
-1 < 15 is true enough
:
We can any odd x greater than -3 will satisfy the statement
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Miscellaneous_Word_Problems/465224: You are given a five gallon pail and a three gallon pail, both of which are unmarked. How can you fetch four gallons of water in one trip?
I am supposed to use both buckets and I am not to estimate an amount because the buckets are not marked. I thought that I could fill the three gallon bucket and put it inside the five gallon bucket and fill the five gallon bucket to the top of the three gallon bucket but I'm not sure that this would give me four gallons. I also thought about fillig both buckets to get eight gallons but I don't think that that is what she's looking for. Help! I'm stuck!
1 solutions
Answer 319032 by ankor@dixie-net.com(15649) on 2011-06-29 06:30:10 (Show Source):
You can put this solution on YOUR website!You are given a five gallon pail and a three gallon pail, both of which are unmarked.
How can you fetch four gallons of water in one trip?
:
How about this?
Fill the 5 gal, pour into the 3 gal to leave 2 gal remaining in the 5 gal pail
Empty the 3 gal pail, pour the the remaining 2 gal into the 3 gal pail
Fill the 5 gal pail, pour 1 gal into the 3 gal pail which has 2 gal in it, which fills it
This leaves exactly 4 gal remaining in the 5 gal pail
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