Questions on Logic: Proofs answered by real tutors!

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Question 170241: find the exact value of
-2log2^4
: find the exact value of
-2log2^4

Click here to see answer by Alan3354(1431) About Me 

Question 167120: Are the multiples of two all prime, all composite, or both?: Are the multiples of two all prime, all composite, or both?
Click here to see answer by Earlsdon(3748) About Me 

Question 164160: 1. What is the maximum value for the function y= 1/3sin5x
a. 1/3
b. 1/5
c. -1/3
d. -5
2. if g(x)=4sin 5x+k, what is the minimum value of g(x)?
a. 4 - k
b. k - 5
c. k
d. k - 4
: 1. What is the maximum value for the function y= 1/3sin5x
a. 1/3
b. 1/5
c. -1/3
d. -5
2. if g(x)=4sin 5x+k, what is the minimum value of g(x)?
a. 4 - k
b. k - 5
c. k
d. k - 4

Click here to see answer by alicealc(23) About Me 

Question 162436This question is from textbook
: P v (Q & R) <=> (P v Q) & (P v R)
This question is from textbook
: P v (Q & R) <=> (P v Q) & (P v R)

Click here to see answer by Edwin McCravy(2086) About Me 

Question 162437This question is from textbook
: Problem:
(P & Q) <=> ~(P -> ~Q)
This question is from textbook
: Problem:
(P & Q) <=> ~(P -> ~Q)

Click here to see answer by Edwin McCravy(2086) About Me 

Question 162438This question is from textbook
: problem 1f:
-(PvQ) -||- -P&-Q
This question is from textbook
: problem 1f:
-(PvQ) -||- -P&-Q

Click here to see answer by vleith(1174) About Me 

Question 160091: Prove the argument:
1. p -> q
2. r \/ s
3. ~s -> ~t
4. ~q \/ s
5. ~s
6. (~p \/ r) -> u
7. w \/ t
therefore u /\ w
: Prove the argument:
1. p -> q
2. r \/ s
3. ~s -> ~t
4. ~q \/ s
5. ~s
6. (~p \/ r) -> u
7. w \/ t
therefore u /\ w

Click here to see answer by Edwin McCravy(2086) About Me 

Question 160240: I don't understand the logic proofs
not k
not l then h
j then k
h then j
therefore l
i understand modus tollens, modus ponens, law of sillogysm and law of contrapositives but not how they apply to a proof as long as the above.
i also don't understand how to do the proofs and reasons, the above has 7 of each
: I don't understand the logic proofs
not k
not l then h
j then k
h then j
therefore l
i understand modus tollens, modus ponens, law of sillogysm and law of contrapositives but not how they apply to a proof as long as the above.
i also don't understand how to do the proofs and reasons, the above has 7 of each

Click here to see answer by stanbon(18999) About Me 

Question 159824This question is from textbook
: Could I ask your help?
Lamps which cost $120 wholesale are sold for $192, at a profit of $6 per lamp. How many lamps were in the shipment?
9
10
11
12
13
This question is from textbook
: Could I ask your help?
Lamps which cost $120 wholesale are sold for $192, at a profit of $6 per lamp. How many lamps were in the shipment?
9
10
11
12
13

Click here to see answer by vleith(1174) About Me 

Question 156521: Adapted from Algebra and Trigonometry by P. Forester but I have a textbook by Holt
Prove the product of two negatives is a positive
(-x)(-y) = (-1*x)(-1*y) Identity
= (-1)[x*(-1)](y) distributive
= (-1)[-1*x](y)
= [-1*(-1)] xy
= 1*xy
= xy
therefore (-x)(-y) = xy
: Adapted from Algebra and Trigonometry by P. Forester but I have a textbook by Holt
Prove the product of two negatives is a positive
(-x)(-y) = (-1*x)(-1*y) Identity
= (-1)[x*(-1)](y) distributive
= (-1)[-1*x](y)
= [-1*(-1)] xy
= 1*xy
= xy
therefore (-x)(-y) = xy

Click here to see answer by stanbon(18999) About Me 

Question 154495: proove that square root of 2 is irrational!: proove that square root of 2 is irrational!
Click here to see answer by AnlytcPhil(958) About Me 

Question 152200: Find the answer to the numbers 1-10 using three numbers 5,6,3.: Find the answer to the numbers 1-10 using three numbers 5,6,3.
Click here to see answer by oscargut(667) About Me 

Question 147603: Can someone help me construct this truth table? P->(P ->(Q ^ P)). Now, does this mean that first, you work the Q^P? or do you work the p-> which is inside the ( ) first. Then do you take the result of whichever is used and connect it with p-> which is oustide the ( ). Do that make sense. I'm confused too.: Can someone help me construct this truth table? P->(P ->(Q ^ P)). Now, does this mean that first, you work the Q^P? or do you work the p-> which is inside the ( ) first. Then do you take the result of whichever is used and connect it with p-> which is oustide the ( ). Do that make sense. I'm confused too.
Click here to see answer by Edwin McCravy(2086) About Me 

Question 147503: symbolize the following argument and then use a truth table to determine whether the argument is valid or invalid.
1. Valerie will go out if and only if she does not have homework.
Valerie did not go out
Therefore, Valerie had homework.
p= (for me) Valerie will go out q= She does not have homework.
premise 1 p<--q premise 2 = p^~q conclusion = p <--> ^~q

Is that correct?
: symbolize the following argument and then use a truth table to determine whether the argument is valid or invalid.
1. Valerie will go out if and only if she does not have homework.
Valerie did not go out
Therefore, Valerie had homework.
p= (for me) Valerie will go out q= She does not have homework.
premise 1 p<--q premise 2 = p^~q conclusion = p <--> ^~q

Is that correct?

Click here to see answer by stanbon(18999) About Me 

Question 146008This question is from textbook
: can you show mwe how to do this
7) (8 pts)
Construct a histogram and a frequency polygon for the following frequency distribution
Miles Number of Commuters
Class Frequency
0 - 24 4
25 - 49 10
50 - 74 11
75 - 99 5
100 –124 1
This question is from textbook
: can you show mwe how to do this
7) (8 pts)
Construct a histogram and a frequency polygon for the following frequency distribution
Miles Number of Commuters
Class Frequency
0 - 24 4
25 - 49 10
50 - 74 11
75 - 99 5
100 –124 1

Click here to see answer by Edwin McCravy(2086) About Me 

Question 146000This question is from textbook
: could you help me; i am stuck. Please
a) A collection of all the objects to be studied is a sample false (population)
b) A subset or part of the subjects to be studied is a sample true
c) In a frequency distribution the class limits must overlap dont know – would say false
d) Pie charts are best used to plot numbers over a period of time false
e) A frequency distribution should have between 3 and 10 classes dont know -woiuld say true
This question is from textbook
: could you help me; i am stuck. Please
a) A collection of all the objects to be studied is a sample false (population)
b) A subset or part of the subjects to be studied is a sample true
c) In a frequency distribution the class limits must overlap dont know – would say false
d) Pie charts are best used to plot numbers over a period of time false
e) A frequency distribution should have between 3 and 10 classes dont know -woiuld say true

Click here to see answer by stanbon(18999) About Me 

Question 145886This question is from textbook
: How can I do this. Any suggestions?
Construct a pie chart for the data and analyze the results. Draw a circle. Cut it into four slices with ratio 62, 18, 12, 8 – Results show most women work because they need the income for family of other purposes.
This question is from textbook
: How can I do this. Any suggestions?
Construct a pie chart for the data and analyze the results. Draw a circle. Cut it into four slices with ratio 62, 18, 12, 8 – Results show most women work because they need the income for family of other purposes.

Click here to see answer by Edwin McCravy(2086) About Me 

Question 145891This question is from textbook
: What do you think about this px? Can you help me on this?
2. (5 pts)
Construct a frequency distribution of the ages that 25 randomly selected smokers started smoking:
26 26 25 17 16 16 14 17 21 16
16 18 17 15 15 19 16 17 22 15
19 17 16 27 16
This question is from textbook
: What do you think about this px? Can you help me on this?
2. (5 pts)
Construct a frequency distribution of the ages that 25 randomly selected smokers started smoking:
26 26 25 17 16 16 14 17 21 16
16 18 17 15 15 19 16 17 22 15
19 17 16 27 16

Click here to see answer by Edwin McCravy(2086) About Me 

Question 145613: How does this work. Could I please get some help?
2. Select five random numbers between 70 and 100. Calculate the mean, median, mode, and midrange of these numbers. Based on your calculations, which measure of central tendency best represents these numbers?
: How does this work. Could I please get some help?
2. Select five random numbers between 70 and 100. Calculate the mean, median, mode, and midrange of these numbers. Based on your calculations, which measure of central tendency best represents these numbers?

Click here to see answer by kristina29(1) About Me 

Question 145605This question is from textbook
: I can't figure this out...could I ask you to help me?? Thank you
13. (4 pts) At an annual flower show, 6 different entries are to be arranged in a row.
a) How many different arrangements of the entries are possible? 6!
b) If the owners of the 1st, 2nd, and 3rd place entries will be awarded prizes of $100, $50, and $25 respectively, how many ways can the prizes be awarded? 6 items taken 3 at a time 6*5*4 = 120 ???

This question is from textbook
: I can't figure this out...could I ask you to help me?? Thank you
13. (4 pts) At an annual flower show, 6 different entries are to be arranged in a row.
a) How many different arrangements of the entries are possible? 6!
b) If the owners of the 1st, 2nd, and 3rd place entries will be awarded prizes of $100, $50, and $25 respectively, how many ways can the prizes be awarded? 6 items taken 3 at a time 6*5*4 = 120 ???


Click here to see answer by solver91311(1877) About Me 

Question 145216This question is from textbook
: I need your help here-please
14. (2 pts) How many different ways are there for an admissions officer to select a group of 7 college candidates from a group of 19 applicants for an interview? 19 * 7 at a time = 19*18*17*16*15*14*13
I am not that strong in this field. Can you look over this stuff AND get me the answers when it is done so I know where i may have goofed up?
This question is from textbook
: I need your help here-please
14. (2 pts) How many different ways are there for an admissions officer to select a group of 7 college candidates from a group of 19 applicants for an interview? 19 * 7 at a time = 19*18*17*16*15*14*13
I am not that strong in this field. Can you look over this stuff AND get me the answers when it is done so I know where i may have goofed up?

Click here to see answer by josmiceli(2035) About Me 
Question 145216This question is from textbook
: I need your help here-please
14. (2 pts) How many different ways are there for an admissions officer to select a group of 7 college candidates from a group of 19 applicants for an interview? 19 * 7 at a time = 19*18*17*16*15*14*13
I am not that strong in this field. Can you look over this stuff AND get me the answers when it is done so I know where i may have goofed up?
This question is from textbook
: I need your help here-please
14. (2 pts) How many different ways are there for an admissions officer to select a group of 7 college candidates from a group of 19 applicants for an interview? 19 * 7 at a time = 19*18*17*16*15*14*13
I am not that strong in this field. Can you look over this stuff AND get me the answers when it is done so I know where i may have goofed up?

Click here to see answer by jim_thompson5910(9376) About Me 

Question 145213This question is from textbook
: I can't figure this. Can you help me.
7. (2 pts)
Two balls are to be selected without replacement from a bag containing one red, one blue, one green, one yellow, and one black ball. How many points are there in the sample space? 5*4 = 20 ??
This question is from textbook
: I can't figure this. Can you help me.
7. (2 pts)
Two balls are to be selected without replacement from a bag containing one red, one blue, one green, one yellow, and one black ball. How many points are there in the sample space? 5*4 = 20 ??

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Question 145212This question is from textbook
: Could you please help me with this? Thank you
1000 tickets for prizes are sold for $2 each. Seven prizes will be awarded – one for $400, one for $200, and five for $50. Steven purchases one of the tickets.
400(1/1000) + 200(1/1000) + 50(5/1000) – 2(993/1000) = -1.14
a) Find the expected value expected value is -$1.14
b) Find the fair price of the ticket. ?????
This question is from textbook
: Could you please help me with this? Thank you
1000 tickets for prizes are sold for $2 each. Seven prizes will be awarded – one for $400, one for $200, and five for $50. Steven purchases one of the tickets.
400(1/1000) + 200(1/1000) + 50(5/1000) – 2(993/1000) = -1.14
a) Find the expected value expected value is -$1.14
b) Find the fair price of the ticket. ?????

Click here to see answer by jim_thompson5910(9376) About Me 

Question 145210This question is from textbook
: I am not sure of this answer; is it corret?
Thank you!
5. (3 pts) 500 raffle tickets are sold at $2 each. One grand prize of $100 and two consolation prizes of $50 will be awarded. Find Jake’s expectation if he purchases one ticket.
100(1/500) + 50*(2/500) – 2*(497/500) = (200-994)/500 = - 1.58
A) -$0.40 B) -$1.20 C) -$1.60 D) $7.75 E) $0.80
This question is from textbook
: I am not sure of this answer; is it corret?
Thank you!
5. (3 pts) 500 raffle tickets are sold at $2 each. One grand prize of $100 and two consolation prizes of $50 will be awarded. Find Jake’s expectation if he purchases one ticket.
100(1/500) + 50*(2/500) – 2*(497/500) = (200-994)/500 = - 1.58
A) -$0.40 B) -$1.20 C) -$1.60 D) $7.75 E) $0.80

Click here to see answer by jim_thompson5910(9376) About Me 

Question 145211This question is from textbook
: Could you help me with this Please?
9. (6 pts) A couple plan to have exactly three children.
(a) Construct a tree diagram and list the sample space.
View this --> http://collabvsl.wetpaint.com/page/Basic+Probability
(b) Find the probability that the family has at least two girls.
This question is from textbook
: Could you help me with this Please?
9. (6 pts) A couple plan to have exactly three children.
(a) Construct a tree diagram and list the sample space.
View this --> http://collabvsl.wetpaint.com/page/Basic+Probability
(b) Find the probability that the family has at least two girls.

Click here to see answer by vleith(1174) About Me 

Question 144253: PLEASE HELP !!!!!
In using mathematical induction to prove 1^2+3^2+5^2=...+(2n-1)^2 =
(n(2n-1)(2n+1)/3), the P k statment is 1^2+3^2+5^2+...+(2k-1)^2 = (k(2k-1)(2k+1)/3)
Is this true or false
THANK YOU
: PLEASE HELP !!!!!
In using mathematical induction to prove 1^2+3^2+5^2=...+(2n-1)^2 =
(n(2n-1)(2n+1)/3), the P k statment is 1^2+3^2+5^2+...+(2k-1)^2 = (k(2k-1)(2k+1)/3)
Is this true or false
THANK YOU

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Question 141682: How many combinations of room decoration can you create with 12 wall papers, 7 floors and 5 drapes? What equation do I need to use to solve this problem? What would be the proof?: How many combinations of room decoration can you create with 12 wall papers, 7 floors and 5 drapes? What equation do I need to use to solve this problem? What would be the proof?
Click here to see answer by checkley77(3639) About Me 

Question 136047: Three geniuses stand in a file (one behind the other). Each can see only to the front, so the rear person can see the middle and the front, the middle person can see the front, and the genius in the front cannot see anyone.

You have five hats. Two are white, and three are red. You blindfold the three geniuses, who are utterly truthful, and put a hat – at random – on the head of each. Then you hide the other two hats and remove the blindfolds.



You then ask each genius to name the color of his hat (which he cannot see).



The rear one says "I don't know." The middle on says, "I don't know." Then the front one says, "I know."



WHAT COLOR IS THE FRONT GENIUS' HAT??????

: Three geniuses stand in a file (one behind the other). Each can see only to the front, so the rear person can see the middle and the front, the middle person can see the front, and the genius in the front cannot see anyone.

You have five hats. Two are white, and three are red. You blindfold the three geniuses, who are utterly truthful, and put a hat – at random – on the head of each. Then you hide the other two hats and remove the blindfolds.



You then ask each genius to name the color of his hat (which he cannot see).



The rear one says "I don't know." The middle on says, "I don't know." Then the front one says, "I know."



WHAT COLOR IS THE FRONT GENIUS' HAT??????


Click here to see answer by jonessk(1) About Me 

Question 131383This question is from textbook Mathematics concepts and skills
: i need help on this question please.This question is from textbook Mathematics concepts and skills
: i need help on this question please.
Click here to see answer by TakeATuition.com(57) About Me 

Question 128145This question is from textbook Discrete Mathematics And Its Applications
: Please assist me in arriving to the answer of this problem.
The problem as stated from the book:
Show that if you pick three socks from a drawer containing just blue socks and black socks, you must get either a pair of blue socks or a pair of black socks.
Given hint by professor:
Either use contradiction or better yet try proof by cases.
I do not understand how to use proofs by contradiction.
This question is from textbook Discrete Mathematics And Its Applications
: Please assist me in arriving to the answer of this problem.
The problem as stated from the book:
Show that if you pick three socks from a drawer containing just blue socks and black socks, you must get either a pair of blue socks or a pair of black socks.
Given hint by professor:
Either use contradiction or better yet try proof by cases.
I do not understand how to use proofs by contradiction.

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Question 127064: Show that the sum of an odd integer and an even integer is an odd integer: Show that the sum of an odd integer and an even integer is an odd integer
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Question 123519This question is from textbook Discrete Mathematics
: Assuming the truth of the theorem that states that √n is irrational whenever n is a positive integer that is not a perfect square, prove that √2 + √3 is irrational.This question is from textbook Discrete Mathematics
: Assuming the truth of the theorem that states that √n is irrational whenever n is a positive integer that is not a perfect square, prove that √2 + √3 is irrational.
Click here to see answer by Edwin McCravy(2086) About Me 

Question 123516This question is from textbook Discrete Mathematics
: Prove that there is a positive integer that can be written as the sum of squares of positive integers in two different ways.This question is from textbook Discrete Mathematics
: Prove that there is a positive integer that can be written as the sum of squares of positive integers in two different ways.
Click here to see answer by Edwin McCravy(2086) About Me 

Question 122289This question is from textbook Mechanics I
: I didnt know what topic this stuff came under, :( so i thought proof maybe....the closest i can find, its a mechanics question.
11. A parcel of mass 60kg is released from rest on a smooth plane inclined at arcsin 0.6 (3/5) to the horizontal. Find the velocity of the parcel when it has travelled 5m down the slope.
I cant do it, can some one help?
What i personally did was,
invsin0.6 = 37, Sin37*9.81*60 = 354 approx.
So Acceleration down the slope is 354ms-2,
v squared = u sqaured + 2as,
so, velocity squared therefore =, 2 * 354 * 5 = 3540, root that = velocity, =59.5...
but the answer is 7.67 :( Please help? with details of how to do, thanks.
This question is from textbook Mechanics I
: I didnt know what topic this stuff came under, :( so i thought proof maybe....the closest i can find, its a mechanics question.
11. A parcel of mass 60kg is released from rest on a smooth plane inclined at arcsin 0.6 (3/5) to the horizontal. Find the velocity of the parcel when it has travelled 5m down the slope.
I cant do it, can some one help?
What i personally did was,
invsin0.6 = 37, Sin37*9.81*60 = 354 approx.
So Acceleration down the slope is 354ms-2,
v squared = u sqaured + 2as,
so, velocity squared therefore =, 2 * 354 * 5 = 3540, root that = velocity, =59.5...
but the answer is 7.67 :( Please help? with details of how to do, thanks.

Click here to see answer by scott8148(2759) About Me 

Question 122291This question is from textbook Mechanics I
: 12. A particle of mass 2kg slides down a rough plane inclined at 20 degrees to the horizontal. Given that the acceleration of the particle is 1.5ms-2, find the coefficient of friction between the particle and the plane.
Thanks for any help, its so hard :D
This question is from textbook Mechanics I
: 12. A particle of mass 2kg slides down a rough plane inclined at 20 degrees to the horizontal. Given that the acceleration of the particle is 1.5ms-2, find the coefficient of friction between the particle and the plane.
Thanks for any help, its so hard :D

Click here to see answer by Fombitz(1755) About Me 

Question 104112: Given angle 1 is =(squiggly line on top of the equal sign) to angle 2
and angle 3 ia =(squiggly line on top of the equal sign) to angle 4
Prove: a is parallel to c
there's a picture and here's a description of what it looks like:
There are 3 horizontal lines, line a is the top most one, line b is in the middle, and line c is the bottom most one, (theses are all horizontal)
Then there are 2 vertical lines going through all three of the horizontal lines. (these vertical lines are kind of slanted).
In between line b and c, there are the numbers 1 and 2. Number 1 is on the left of the vertical line that is closest to b and c and it is under line b in the top left side of the vertical line. and number 2 is the opposite of number 1,(i think these are alternate interior angles or numbers).
Then there's a number 3 located on the other vertical line, that is going through line a. the number 3 is on top of line a, and to the right of the second vertical line going through all three horizontal lines.
Lastly number 4 is located under line b, but to the right of the 2nd vertical line. So that it is corresponding to number 1.
Please help me prove this problem.
: Given angle 1 is =(squiggly line on top of the equal sign) to angle 2
and angle 3 ia =(squiggly line on top of the equal sign) to angle 4
Prove: a is parallel to c
there's a picture and here's a description of what it looks like:
There are 3 horizontal lines, line a is the top most one, line b is in the middle, and line c is the bottom most one, (theses are all horizontal)
Then there are 2 vertical lines going through all three of the horizontal lines. (these vertical lines are kind of slanted).
In between line b and c, there are the numbers 1 and 2. Number 1 is on the left of the vertical line that is closest to b and c and it is under line b in the top left side of the vertical line. and number 2 is the opposite of number 1,(i think these are alternate interior angles or numbers).
Then there's a number 3 located on the other vertical line, that is going through line a. the number 3 is on top of line a, and to the right of the second vertical line going through all three horizontal lines.
Lastly number 4 is located under line b, but to the right of the 2nd vertical line. So that it is corresponding to number 1.
Please help me prove this problem.

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Question 98350: prove that 1+3sqrt(3) is irrational
1 + 3* 1.732050808
1+ 5.196152423
6.196152423
: prove that 1+3sqrt(3) is irrational
1 + 3* 1.732050808
1+ 5.196152423
6.196152423

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Question 99157: How do you construct a formal proof for the following argument:
A ^ (B v C) to conclude with the goal, (A ^ B) v (A ^C)?
: How do you construct a formal proof for the following argument:
A ^ (B v C) to conclude with the goal, (A ^ B) v (A ^C)?

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Question 97605: I want to know the next four letters of this pattern: T,F,S,N,E,T: I want to know the next four letters of this pattern: T,F,S,N,E,T
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Question 83901This question is from textbook Introduction to Logic
: This question is from textbook Introduction to Logic
:
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Question 74408: Prove that for any sets A and B, if A is a subset of B, then
Help! Thanks!
: Prove that for any sets A and B, if A is a subset of B, then
Help! Thanks!

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Question 69325: What would be the couterexample to the statement below?
If the sum of two integers is even, then both of the integers are even.
: What would be the couterexample to the statement below?
If the sum of two integers is even, then both of the integers are even.

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Question 66567: Two cars leave town going in the same direction. One travels 55 mph and the other travels 65 mph How long will it take before they are 180 miles apart?
Hint: This is different from problem #3, because we do not know the total distance. We do know that one car is 180 miles ahead of the other, so the slow car's distance can be represented by " d " and the distance of the fast car, which would be ahead, can be represented by "d + 180." The time is the same again, and can be represented by "t." This time we have two unknowns, so we need two equations, one for the fast car, and one for the slow car. Again we are using the basic formula d = rt , and substituting the values that are relevant to our situation. The equation for the slow car is: d = 55t. You write the equation for the fast car, and solve the system by substitution. Don't forget the units in your answer.
: Two cars leave town going in the same direction. One travels 55 mph and the other travels 65 mph How long will it take before they are 180 miles apart?
Hint: This is different from problem #3, because we do not know the total distance. We do know that one car is 180 miles ahead of the other, so the slow car's distance can be represented by " d " and the distance of the fast car, which would be ahead, can be represented by "d + 180." The time is the same again, and can be represented by "t." This time we have two unknowns, so we need two equations, one for the fast car, and one for the slow car. Again we are using the basic formula d = rt , and substituting the values that are relevant to our situation. The equation for the slow car is: d = 55t. You write the equation for the fast car, and solve the system by substitution. Don't forget the units in your answer.

Click here to see answer by venugopalramana(3286) About Me