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# Recent problems solved by 'stanbon'

Jump to solutions: 0..29 , 30..59 , 60..89 , 90..119 , 120..149 , 150..179 , 180..209 , 210..239 , 240..269 , 270..299 , 300..329 , 330..359 , 360..389 , 390..419 , 420..449 , 450..479 , 480..509 , 510..539 , 540..569 , 570..599 , 600..629 , 630..659 , 660..689 , 690..719 , 720..749 , 750..779 , 780..809 , 810..839 , 840..869 , 870..899 , 900..929 , 930..959 , 960..989 , 990..1019 , 1020..1049 , 1050..1079 , 1080..1109 , 1110..1139 , 1140..1169 , 1170..1199 , 1200..1229 , 1230..1259 , 1260..1289 , 1290..1319 , 1320..1349 , 1350..1379 , 1380..1409 , 1410..1439 , 1440..1469 , 1470..1499 , 1500..1529 , 1530..1559 , 1560..1589 , 1590..1619 , 1620..1649 , 1650..1679 , 1680..1709 , 1710..1739 , 1740..1769 , 1770..1799 , 1800..1829 , 1830..1859 , 1860..1889 , 1890..1919 , 1920..1949 , 1950..1979 , 1980..2009 , 2010..2039 , 2040..2069 , 2070..2099 , 2100..2129 , 2130..2159 , 2160..2189 , 2190..2219 , 2220..2249 , 2250..2279 , 2280..2309 , 2310..2339 , 2340..2369 , 2370..2399 , 2400..2429 , 2430..2459 , 2460..2489 , 2490..2519 , 2520..2549 , 2550..2579 , 2580..2609 , 2610..2639 , 2640..2669 , 2670..2699 , 2700..2729 , 2730..2759 , 2760..2789 , 2790..2819 , 2820..2849 , 2850..2879 , 2880..2909 , 2910..2939 , 2940..2969 , 2970..2999 , 3000..3029 , 3030..3059 , 3060..3089 , 3090..3119 , 3120..3149 , 3150..3179 , 3180..3209 , 3210..3239 , 3240..3269 , 3270..3299 , 3300..3329 , 3330..3359 , 3360..3389 , 3390..3419 , 3420..3449 , 3450..3479 , 3480..3509 , 3510..3539 , 3540..3569 , 3570..3599 , 3600..3629 , 3630..3659 , 3660..3689 , 3690..3719 , 3720..3749 , 3750..3779 , 3780..3809 , 3810..3839 , 3840..3869 , 3870..3899 , 3900..3929 , 3930..3959 , 3960..3989 , 3990..4019 , 4020..4049 , 4050..4079 , 4080..4109 , 4110..4139 , 4140..4169 , 4170..4199 , 4200..4229 , 4230..4259 , 4260..4289 , 4290..4319 , 4320..4349 , 4350..4379 , 4380..4409 , 4410..4439 , 4440..4469 , 4470..4499 , 4500..4529 , 4530..4559 , 4560..4589 , 4590..4619 , 4620..4649 , 4650..4679 , 4680..4709 , 4710..4739 , 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56970..56999 , 57000..57029 , 57030..57059 , 57060..57089 , 57090..57119 , 57120..57149 , 57150..57179 , 57180..57209 , 57210..57239, >>Next

 Inequalities/108963: Copy and complete the sataement using <,> or = 34. 8^8 ___ 8^6 x 8 Any help with this equation would be greatly appreciated1 solutions Answer 79453 by stanbon(57304)   on 2007-11-09 09:35:52 (Show Source): You can put this solution on YOUR website!8^8 ___ 8^6 x 8 8^8 ____8^(6+1) 8^8 ____8^7 8^8 > 8^7 =========== Cheers, Stan H.
 Inequalities/108965: Copy and complete the sataement using <,> or = A square has a side length of 2x^4 centimeters. Represent the area of the square using exponents. Any help with this equation would be greatly appreciated1 solutions Answer 79451 by stanbon(57304)   on 2007-11-09 09:33:56 (Show Source): You can put this solution on YOUR website!A square has a side length of 2x^4 centimeters. Represent the area of the square using exponents. ---------- Formula: Area of a square = (side)^2 Your Problem: Area = (2x^4)^2 Area = (2^2)(x^8) ============ Cheers, Stan H.
 Inequalities/108964: Copy and complete the sataement using <,> or = 3^7 x 3^4 ____ 3^10 Any help with this equation would be greatly appreciated1 solutions Answer 79450 by stanbon(57304)   on 2007-11-09 09:30:45 (Show Source): You can put this solution on YOUR website!Copy and complete the sataement using <,> or = 3^7 x 3^4 ____ 3^10 3^(7+4)_______ 3^10 3^11 _________ 3^10 3^11 > 3^10 ============ Cheers, Stan H.
 Graphs/108933: This question is from textbook x-3=y i dont know how to graph this using intercepts 1 solutions Answer 79428 by stanbon(57304)   on 2007-11-08 22:44:05 (Show Source): You can put this solution on YOUR website!x-3=y Let x = 0, then y = -3 Let y = 0, then x = 3 ------------- Plot the points (0,-3) and (3,0) --------------- Graph: Cheers, Stan H.
 Expressions-with-variables/108932: This question is from textbook Prentice Hall Mathematics Geomerty Louisiana 5x-20+3x-2=1801 solutions Answer 79427 by stanbon(57304)   on 2007-11-08 22:39:08 (Show Source): You can put this solution on YOUR website!5x-20+3x-2=180 8x - 22 = 180 8x = 202 x = 25.25 ================ Cheers, Stan H.
 Trigonometry-basics/108931: Complete each of the following statements, using the symbol < or >. HELP 5/16 ? 0.313 1 solutions Answer 79426 by stanbon(57304)   on 2007-11-08 22:36:38 (Show Source): You can put this solution on YOUR website!using the symbol < or >. HELP 5/16 ? 0.313 5/16 = 0.3125 --------------- Therefore 5/16 < 0.313 ============== Cheers, Stan H.
 Mixture_Word_Problems/108929: The Quick Mart has two kinds of nuts. Pecans sell for \$1.55 per pound and walnuts sell for \$1.95 per pound. How many pounds of walnuts must be added to 15 pounds of pecans to make a mixture that sells for \$1.75 per pound?1 solutions Answer 79425 by stanbon(57304)   on 2007-11-08 22:32:24 (Show Source): You can put this solution on YOUR website!Pecans sell for \$1.55 per pound and walnuts sell for \$1.95 per pound. How many pounds of walnuts must be added to 15 pounds of pecans to make a mixture that sells for \$1.75 per pound? ----------------- Pecan DATA: Amt = 15 lbs ; Value is 1.55*15 = 23.25 dollars ------------ Walnut DATA: Amt = x lbs ; value is 1.95x dollars ------------- Mixture DATA: Amt = 15+x lbs ; value = 1.75(15+x) = 26.25 + 1.75x dollars -------------- EQUATION: value + value = value 23.25 + 1.95x = 26.25+1.5x 0.45x = 3 x = 6 2/3 lbs (amount of walnuts tht must be added to make the mix) ================= Cheers, Stan H.
 Travel_Word_Problems/108903: WORD PROBLEM BUSINESS A ELECTRONICS STORE WANTS TO ORDER AT LEAST 3 TIMES AS MANY DVD PLAYERS AS VHS PLAYERS. WRITE AN INEQUALITY EXPRESSING THIS RELATIONSHIP. THANKS JMS1 solutions Answer 79412 by stanbon(57304)   on 2007-11-08 20:49:14 (Show Source): You can put this solution on YOUR website!A ELECTRONICS STORE WANTS TO ORDER AT LEAST 3 TIMES AS MANY DVD PLAYERS AS VHS PLAYERS. WRITE AN INEQUALITY EXPRESSING THIS RELATIONSHIP. -------------- Let # of DVD players be D. Let # of VHS players be V. ------------ INEQUALITY: D >= V ============= Cheers, Stan H.
 Expressions-with-variables/108881: This question is from textbook I am having trouble finding the steps to solve this problem. 2Q^3 -11Q^2 -100=0. My text give me the answer of Q=6.64 but not the steps to solve it which I will need to solve other problems. Please help.1 solutions Answer 79410 by stanbon(57304)   on 2007-11-08 20:45:28 (Show Source): You can put this solution on YOUR website!solve this problem. 2Q^3 -11Q^2 -100=0. My text give me the answer of Q=6.64 -------------- I graphed the cubic and found a zero at x = 6.6355693... using a TI-83 graphing calculator. It is the only Real Number zero. =========== Cheers, Stan H.
 Linear-systems/108869: Combine like terms. 6a2 + 4a + 5 + 3a2 + 7a – 2 1 solutions Answer 79408 by stanbon(57304)   on 2007-11-08 20:30:16 (Show Source): You can put this solution on YOUR website!Combine like terms. 6a2 + 4a + 5 + 3a2 + 7a – 2 --------- = 9a^2+11a+3 ==================== Cheers, stan H.
 Polynomials-and-rational-expressions/108890: Why is 6r squared -18rs+ 3 over s not a polynomial?1 solutions Answer 79398 by stanbon(57304)   on 2007-11-08 19:53:48 (Show Source): You can put this solution on YOUR website!Why is 6r squared -18rs+ 3 over s not a polynomial? (6r^2-18rs+3)/s = (6r^2/s)-(18r) + (3/s) = 6r^2s^-1 - 18r +3s^-1 Terms with negative exponents are not permitted in polynomials. Cheers, Stan H.
 Miscellaneous_Word_Problems/108797: I am stuck on a few problems. If at all possible could someone please help me thank you. 1. The tax increase is more than \$7890. 2. Find the area of a triangle whose altitude is 7 feet and whose base is 22 feet. 3. Four less than nine times a number is one hundred twenty-two. Find teh original number.1 solutions Answer 79359 by stanbon(57304)   on 2007-11-08 15:37:58 (Show Source): You can put this solution on YOUR website!1. The tax increase is more than \$7890. Let "t" be the tax increase. t > 7890 ==================== 2. Find the area of a triangle whose altitude is 7 feet and whose base is 22 feet. Area = (1/2)(base)(height) Area = (1/2)(22')(7') Area = 77 sq. ft. ------------------ 3. Four less than nine times a number is one hundred twenty-two. Find the original number. Let the number be "x". EQUATION: 9x-4 =122 9x = 126 x = 14 =============== Cheers, Stan H.
 Polynomials-and-rational-expressions/108811: Simplify and evaluate: (x^3y^-4z^0/5x^6y8)^31 solutions Answer 79358 by stanbon(57304)   on 2007-11-08 15:33:19 (Show Source): You can put this solution on YOUR website!Simplify and evaluate: (x^3y^-4z^0/5x^6y^8)^3 Simplify: [(x^3y^-4) / (5x^6y^8)]^3 Simplify: [1 / 5x^3 y^12]^3 = 1/[125x^3y^12] ================= Cheers, Stan H.
 Polynomials-and-rational-expressions/108821: Please can you help me with this equation? 3y^2-12 /4y^2+4y+4 divided by y^3-2y^2/ Y^2+2y 1 solutions Answer 79353 by stanbon(57304)   on 2007-11-08 15:26:01 (Show Source): You can put this solution on YOUR website![(3y^2-12) /(4y^2+4y+4)] / [(y^3-2y^2) / (Y^2+2y)] Factor where you can: = [3y(y-4) / 4(y^2+y+1)] / [y^2(y-2) / y(y+2)] Cancel any factor common to a numerator and a denominator such as "y": = [3y(y-4) / 4(y^2+y+1)] / [y(y-2) / (y+2)] Invert the denominator and multiply: = [3y(y-4) / 4(y^2+y+1)] * [(y+2)/ y(y-2) ] ----------- Cancel any factor common to a numerator and a denominator such as "y": -------------- = [3(y-4)(y+2)] / [4(y^2+y+1)(y-2)] ====================== Cheers, Stan H.
 Points-lines-and-rays/108833: is the points A(2,1),B(-4,1),C(-1,-3) Collinear or noncollinear1 solutions Answer 79349 by stanbon(57304)   on 2007-11-08 15:16:15 (Show Source): You can put this solution on YOUR website!If the slopes from point to point are all the same the points are collinear. ----------------- is the points A(2,1),B(-4,1),C(-1,-3) Collinear or noncollinear --------------- from A to B: slope = 0 from B to C; slope = (-3-1)/(-1--4) = -4/3 ---------------- slopes are not the same so the points are not collinear =============== Cheers, Stan H.
 Polynomials-and-rational-expressions/108826: We just started factoring polynomials and I don't understand how you can tell if a problem when you first look at it,doesn't have a greater common factor.For example my teacher had this one:21x-7 and another one was:x^9y^6-x^7y^5+x^4y^4+x^3y^3 This so confusing to me,if you could help I would really appreciate it.Thank you in advance JH1 solutions Answer 79347 by stanbon(57304)   on 2007-11-08 15:12:33 (Show Source): You can put this solution on YOUR website!how you can tell if a problem when you first look at it,doesn't have a greater common factor.For example my teacher had this one: 21x-7 You have to see that 21 is the product of 3 and 7 You have to see that you have two terms: 21x and -7 Then you might see that "7" is a factor common to both terms So, you "factor out" the 7 by dividing each term by 7 to get: 7(3x-1) ==================== x^9y^6 - x^7y^5 + x^4y^4 + x^3y^3 Checking the four terms you have to see there is a common factor of x^3 in each term and a common factor of y^3 in each term. Divide each terms by x^3y^3 to get: x^3y^3 (x^6x^3 -x^4y^3 +xy + 1) ================ Hope that helps. Cheers, Stan H.
 Polynomials-and-rational-expressions/108829: Question #107885 example 1 in your list: 6x^2 - xy - 5y^2. I need to see steps so that I understand how this was done to repeat it on my other problems.1 solutions Answer 79344 by stanbon(57304)   on 2007-11-08 15:06:39 (Show Source): You can put this solution on YOUR website!6x^2 - xy - 5y^2 Using the AC Method: You need to think of two numbers whose product is AC = 6*-5=-30 and whose sum is B=-1 ------------------ The numbers are -6 and 5 ------------------------ Rewrite the problem substituting -6+5 for -1 6x^2 -6xy+5xy -5y^2 --------------- Factor and 1st two terms and the last two terms separately: 6x(x-y) + 5y(x-y) Factor again: (x-y)(6x+5y) ============== Cheers, Stan H.
 Exponents-negative-and-fractional/108832: Express to a positive exponent then find its value (2/3)^-21 solutions Answer 79342 by stanbon(57304)   on 2007-11-08 15:01:11 (Show Source): You can put this solution on YOUR website!Express to a positive exponent then find its value (2/3)^-2 The negative sign in the exponent means "invert" -------------- So, (2/3)^-2 = (3/2)^2 = 9/4 ------------ Cheers, Stan H.
 Travel_Word_Problems/108830: A passenger train can travel 325 mi in the same time a freight train can take to travel 200 miles. If the speed of the passenger train is 25 mi/h faster then the speed of the freight train, find the speed of each.1 solutions Answer 79340 by stanbon(57304)   on 2007-11-08 14:59:33 (Show Source): You can put this solution on YOUR website!A passenger train can travel 325 mi in the same time a freight train can take to travel 200 miles. If the speed of the passenger train is 25 mi/h faster then the speed of the freight train, find the speed of each. ---------- Passenger train DATA: distance =325 miles ; rate = x mph; time = d/r = 325/x hrs. ----------------- Freight train DATA: distance = 200 miles ; rate = x-25 mph time = d/r = 200/(x-25) hrs ------------------ EQUATION: time = time 325/x = 200/(x-25) 65/x = 40/(x-25) 65(x-25) = 40x 65x - 65*25 = 40x 25x = 65*25 x = 65 mph (speed of the passenger train) x-25 = 40 mph (speed of the freight train) ================= Cheers, Stan H.
 Rational-functions/108831: This question is from textbook Intermediate Algebra Problem #1 Solve: (x+3)(x-5)<0 Problem #2 Weight on Mars: The weight M of an object on Mars varies directly as its weight E on Earth. A person who weighs 95 lbs on Earth weights 38 lbs on Mars. How much would a 100 lb person weigh on Mars 1 solutions Answer 79335 by stanbon(57304)   on 2007-11-08 14:48:19 (Show Source): You can put this solution on YOUR website!Solve: (x+3)(x-5)<0 Draw a number line and label the points x = -3 and x=5 They divide the line into three intervals; you need to determine which intervals contain solutions to your inequality. Pick a "test" value from each interval to check in the inequality, as follows: x=-4, (-4+3)(-4-5) = -1*-9 = 9 >0 so no solutions in (-inf,-3) x= 0, (0+3)(0-5)=-15<0, so the interval (-3,5) is part of the solution. x=6, (6+3)(6-5)=9>0, so no solutions in (5,+inf) ----------------- Solution: the interval (-3,5) ============== ---------- Problem #2 Weight on Mars: The weight M of an object on Mars varies directly as its weight E on Earth. A person who weighs 95 lbs on Earth weights 38 lbs on Mars. How much would a 100 lb person weigh on Mars --------------- Use a proportion: Let "x" be wt. of a 100 lb person on Mars x/100 = 38/95 x = 100*0.4 = 40 lbs. ============== Cheers, Stan H.
 Exponential-and-logarithmic-functions/108805: The problem is: 5+ ln x^2 = 4 I have absolutely no clue how to solve this problem. Please and thank you in advance.1 solutions Answer 79330 by stanbon(57304)   on 2007-11-08 14:12:43 (Show Source): You can put this solution on YOUR website!5+ ln x^2 = 4 ---------------- ln x^2 = -1 2lnx = -1 lnx = -1/2 x = e^(-1/2) x = 0.60653... Cheers, Stan H.
 Quadratic_Equations/108823: Identify the axis of symmetry, create a suitable table of values and sketch the graph(including axis of symmetry). Y=x^2-5x+3 I would appreciate any help on this. 1 solutions Answer 79329 by stanbon(57304)   on 2007-11-08 14:08:59 (Show Source): You can put this solution on YOUR website!Identify the axis of symmetry, create a suitable table of values and sketch the graph(including axis of symmetry). Y=x^2-5x+3 ================ x^2-5x+3 = y Complete the square on the x-terms and keep the equation balanced: x^2-5x+(5/2)^2 = y-3 + (5/2)^2 Factor to get: (x-(5/2))^2 = y+13/4 -------------- Axis of symmetry: x = 5/2 Sketch as a vertical line passing thru all point where x = 5/2 ---------------- graph: ----------------- Table: Y=x^2-5x+3 If x= 1 y=1-5+3 = -1 If x=2 y = 4-10+3= -3 If x=3 y = 9-15+3 -3 If x=4 y = 16-20+3 = -1 ================ Cheers, Stan H.
 Polynomials-and-rational-expressions/108825: We just started factoring polynomials,and I don't understand when you first look at a problem,how to tell if it (doesn't) have a greater common factor.Could you please show me some examples of some that don't have a greater common factor,and how to work them out.I appreciate your time on this,because I need all the help I can get.Thanks again,JH1 solutions Answer 79327 by stanbon(57304)   on 2007-11-08 14:00:56 (Show Source): You can put this solution on YOUR website!Post a few of your problems so we can see at level you are working. Cheers, Stan H.
 Quadratic_Equations/108819: solve using quadratic equation 4x²+7x-15=01 solutions Answer 79314 by stanbon(57304)   on 2007-11-08 13:10:01 (Show Source): You can put this solution on YOUR website!solve using quadratic equation 4x²+7x-15=0 x = [-7 +- sqrt(49-4*4*-15)]/8 x = [ -7 +- sqrt289)]/8 x = [-7 +- 17]/8 x = -24/8 or x = 10/8 x = -3 or x = 5/4 ==================== Cheers, Stan H.
 Exponential-and-logarithmic-functions/108817: Express Log functions as exponentil functions: a. Log m = 3 my answer:3 b. log 5 =y c. ln b =2 For B and C I'm extremely unsure of how to do them, I do not even know where to start. Thank you for your help.1 solutions Answer 79313 by stanbon(57304)   on 2007-11-08 13:06:11 (Show Source): You can put this solution on YOUR website!Express Log functions as exponentil functions: a. Log m = 3 my answer:3 b. log 5 =y c. ln b =2 ---------------- When you see logx = y you are saying "the exponent is y" Keep in mind: log means "exponent" or "power" ----------------- a. log m = 3 means "the exponent is 3" m = 10^3 is the corresponding exponential equation. ============== b. log 5 = y means "the exponent is y" 5 = 10^y is the corresponding exponential equation. ------------- c. ln b = 2 means "the exponent is 2" b = e^2 ============= Cheers, Stan H.
 Expressions-with-variables/108753: This question is from textbook Under certain conditions, the power P, in watts per hour, generated by a windmill with winds blowing v miles per hour is given by P(v)= 0.015v^3 a) find the power generated by 15-mph b) how fast must the wind blow in order to generate 120 watts of power in one hour? I put in 15 for x on the first part. second part I left the equation solved for a and divided by 120. I don't think this resulted the correct answers, help.1 solutions Answer 79289 by stanbon(57304)   on 2007-11-08 08:18:12 (Show Source): You can put this solution on YOUR website!the power P, in watts per hour, generated by a windmill with winds blowing v miles per hour is given by P(v)= 0.015v^3 a) find the power generated by 15-mph P(15) = 0.015v^3 = 0.015(15^3) = 50.625 watts ------------------------- b) how fast must the wind blow in order to generate 120 watts of power in one hour? 120 = 0.015v^3 120/0.015 = v^3 v = 20 mph ============= Cheers, Stan H.
 Travel_Word_Problems/108722: Gina traveled 450 miles to her grandmother's house in two days. She traveled 50 more miles on Saturday than on Sunday. How many miles did she travel on Saturday? on Sunday?1 solutions Answer 79263 by stanbon(57304)   on 2007-11-07 23:03:01 (Show Source): You can put this solution on YOUR website!Gina traveled 450 miles to her grandmother's house in two days. She traveled 50 more miles on Saturday than on Sunday. How many miles did she travel on Saturday? on Sunday? ---------- Let distance traveled on Sunday be "x" miles Then distance traveled on Saturday is "x+50" ---------------- EQUATION: x + x+50 = 450 miles 2x = 400 x = 200 (distance traveled on Sunday) x+50 = 250 (distance traveled on Saturday) ============== Cheers, Stan H.
 Human-and-algebraic-language/108713: I am trying to help my daughter with her Algebra homework and it has been years since I've done a problem of this type. I would appreciate it if you could give me some direction on how to solve this word problem: "Aaron, Beth, Candace, Darvel and Emil ran around a track as part of a fundraiser for their school. Aaron ran first, and then when he was tired, Beth ran. When Beth got tired, Candace ran, and so on. By the end of the fundraiser, they had run a total of 30 miles. Aaron and Beth combined ran 40 percent of the total distance. Beth and Candace combined ran 34 percent of the total distance. Candace and Darvel combined ran 40 percent of the total distance. And Darvel and Emil combined ran 41 percent of the total distance. How far did each person run?" This problem was on a worksheet from the teacher that said "Solve It Problem!" at the top of the page. My daughter thinks her teacher got it from a math magazine but we're not sure which one. Please help me help her get this solved. Thank you so much!1 solutions Answer 79261 by stanbon(57304)   on 2007-11-07 22:53:04 (Show Source): You can put this solution on YOUR website!Aaron, Beth Candance, John and Pat ran around a track as part of a fundraiser for their school Aaron ran first and then when he was tired, Beth ran. When Beth got tired, Candace ran, and so on. By the end of the fundraiser, they had run a total of 30 miles. Aaron and Beth combined ran 40% of the total distance. A + B = 12 miles Beth and Candace combined ran 34% of the total distance. B + C = 10.2 miles Candace and John combined ran 40% of the total distance. C + J = 12 miles John and Pat combined ran 41% of the total distance. J + P = 12.3 miles How far did each person run? -------------------- A + B + C + J + P = 30 A + (10.2-C) + C + J + (12.3-J) = 30 A + 10.2 + 12.3 = 30 A = 7.5 miles B = 12 - 7.5 = 4.5 miles C = 10.2 - 4.5 = 5.7 miles J = 12 - 5.7 ] = 6.3 miles P = 12.3 - 6.3 = 6 miles ================= Cheers, Stan H.
 Travel_Word_Problems/108719: A rabbit is 30 feet from its burrow. It can run 25 feet per second. A coyote that can run 50 feet per second spots the rabbit and starts running towards it. How can i write an expression and an equation to solve for the time it will take the rabbit to reach its burrow and the time for the coyote to get to the burrow?1 solutions Answer 79260 by stanbon(57304)   on 2007-11-07 22:42:01 (Show Source): You can put this solution on YOUR website!A rabbit is 30 feet from its burrow. It can run 25 feet per second. A coyote that can run 50 feet per second spots the rabbit and starts running towards it. How can i write an expression and an equation to solve for the time it will take the rabbit to reach its burrow and the time for the coyote to get to the burrow? ------------------ Rabbit DATA: rate = 25 ft/sec ; distance = 30 ft; time = d/r = 30/25 = 6/5 seconds ---------------- Coyote DATA: rate = 50 ft/sec ; distance = x ft ; time = d/r = x/50 seconds ------------------------ With this DATA you could determine the distance at which the coyote could catch the rabbit before it reaches its burrow. That equation would be x/50< 6/5 x < 60 ft ============= Cheers, Stan H.
 Proportions/108715: A certain preparation consists of liquids x, y, and z in the proportion 5:2:1. How many gallons of the preparation can be made from a stock of materials consisting of 25 gallons of x, 20 gallons of y, and 8 gallons of z?1 solutions Answer 79258 by stanbon(57304)   on 2007-11-07 22:30:51 (Show Source): You can put this solution on YOUR website!A certain preparation consists of liquids x, y, and z in the proportion 5:2:1. How many gallons of the preparation can be made from a stock of materials consisting of 25 gallons of x, 20 gallons of y, and 8 gallons of z ? ---------------- Let amount of x be 25 gallons Since amount of x to z is 5 to 1 amount of z is (1/5)x = 5 gallons Since amount of y to z is 2 to 1 amount of y is 2z = 10 gallons ===================== Cheers, Stan H.
 Travel_Word_Problems/108716: This equation has 2 parts to it. Two friends are 60 miles apart. They ride their bicycles to meet each other. Sally starts from the college and heads east riding at a rate of 21 miles per hour. At the same time, Teresa starts from the river and heads west, riding at a rate of 15 miles per hour. a: How far does each cyclist ride in t hours? b: When the two cyclists meet, what must be true about the distances they have ridden? Write and solve an equation to find when they meet1 solutions Answer 79257 by stanbon(57304)   on 2007-11-07 22:20:55 (Show Source): You can put this solution on YOUR website!Two friends are 60 miles apart. They ride their bicycles to meet each other. Sally starts from the college and heads east riding at a rate of 21 miles per hour. At the same time, Teresa starts from the river and heads west, riding at a rate of 15 miles per hour. a: How far does each cyclist ride in t hours? Sally rides 21t miles Teresa rides 15t miles ----------------------- b: When the two cyclists meet, what must be true about the distances they have ridden? Write and solve an equation to find when they meet EQUATION: 21t + 15t = 60 36t = 60 t = 5/3 hrs. They both drove for 5/3 hours. ============ Cheers, Stan H.