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 Angles/472630: The difference between the degree measures of two supplementary angles is 80. Find the degree measure of the larger of the two angles.1 solutions Answer 323993 by ankor@dixie-net.com(15667)   on 2011-07-20 21:45:26 (Show Source): You can put this solution on YOUR website!The difference between the degree measures of two supplementary angles is 80. Find the degree measure of the larger of the two angles. : two angles, a & b, a is the larger a + b = 180 a - b = 80 ------------adding eliminates b, find a 2a = 260 a = a = 130 degrees is the larger angle
 Proportions/472609: 18 men can dig a ditch in 10 days. After they have worked for 4 days how many more men shall be employed to complete the work in 4 days from then?1 solutions Answer 323992 by ankor@dixie-net.com(15667)   on 2011-07-20 21:41:11 (Show Source): You can put this solution on YOUR website!18 men can dig a ditch in 10 days. After they have worked for 4 days how many more men shall be employed to complete the work in 4 days from then? : Determine the no. of man-days required to do the job 18 * 10 = 180 man-days : Let m = no. of additional men required to complete the job in 4 more days The original 18 men will work a total of 8 days : (18*8) + 4m = 180 144 + 4m = 180 4m = 180 - 144 4m = 36 m = m = 9 men required : : Check this by finding the total man-days 18*8 + 9*4 = 180
 Linear-systems/472581: A company makes 3 types of cables. Cable A requires 3 black, 3 white, and 2 red wires. B requires 1 black, 2 white, and 1 red. C requires 2 black, 1 white, and 2 red. They used 100 black, 110 white, and 90 red wires. How many of each cable were made?1 solutions Answer 323991 by ankor@dixie-net.com(15667)   on 2011-07-20 21:22:49 (Show Source): You can put this solution on YOUR website!A company makes 3 types of cables. Cable A requires 3 black, 3 white, and 2 red wires. B requires 1 black, 2 white, and 1 red. C requires 2 black, 1 white, and 2 red. They used 100 black, 110 white, and 90 red wires. How many of each cable were made?: Let a = no. of A cables Let b = no. of B cables Let c = no. of C cables : Write an equation for each color wire black: 3a + b + 2c = 100 white: 3a + 3b + c = 110 red::: 2a + b + 2c = 90 : Note that using the first and 3rd equation we can eliminate b and c 3a + b + 2c = 100 2a + b + 2c = 90 -------------------subtraction eliminates b and c, find a a = 10 type A cables : replace a with 10 in the 1st equation 3(10) + b + 2c = 100 b + 2c = 100 - 30 b + 2c = 70 b = (70-2c); we can use this form for substitution : Do the same with the 2nd equation 3(10) + 3b + c = 110 3b + c = 110 - 30 3b + c = 80 Replace b with (70-2c) 3(70-2c) + c = 80 210 - 6c + c = 80 -6c + c = 80 - 210 -5c = -130 c = c = +26 C type cables : Find b b = 70 - 2c b = 70 - 2(26) b = 70 - 52 b = 18 B type cables : : Check this in the red equation 2a + b + 2c = 90 2(10) + 18 + 2(26) = 20 + 18 + 52 = 90, confirms our solutions of a=10, b=18, c=26
 Travel_Word_Problems/472436: Roma Sherry drove 168 miles from her hometown to the city. During her return trip, she was able to increase her speed by 14 mph. If her return trip took 2 hours less time, find her original speed and speed returning home.1 solutions Answer 323981 by ankor@dixie-net.com(15667)   on 2011-07-20 20:05:12 (Show Source): You can put this solution on YOUR website!Sherry drove 168 miles from her hometown to the city. During her return trip, she was able to increase her speed by 14 mph. If her return trip took 2 hours less time, find her original speed and speed returning home. : Let s = speed to the city then (s+14) = speed home : Write a time equation, time = dist/speed : To city time - return time = 2 hrs - = 2 : Multiply by s(s+14), results: 168(s+14) - 168s = 2s(s+14) : 168s + 2352 - 168s = 2s^2 + 28s : A quadratic equation 2s^2 + 28s - 2352 = 0 : Simplify divide by 2 s^2 + 14s - 1176 = 0 : You can use the quadratic formula, a=1, b=14, c=-1176, but this will factor to: (s+42)(s-28) = 0 The positive solution s = 28 mph to the city then 28+14 = 42 mph return home : : Check this by finding the times 168/28 = 6 hrs 168/42 = 4 hrs --------------- differs: 2 hrs; confirms our solutions
 Complex_Numbers/472190: can someone help me please? im really stuck simplify each complex fraction. 2/c+1 - 1 over 2 + 5/c+11 solutions Answer 323977 by ankor@dixie-net.com(15667)   on 2011-07-20 19:43:27 (Show Source): You can put this solution on YOUR website!simplify each complex fraction. - 1 ------------- 2 + : Put each over a single denominator ------------- : Combine like terms ------------- : ------------- : Invert the dividing fraction and multiply, cancel (c+1) * =
 Mixture_Word_Problems/472377: How many litres of a 30% acid solution should be added to 20 litres of 60% acid solution in order to obtain a 50% acid solution? 1 solutions Answer 323942 by ankor@dixie-net.com(15667)   on 2011-07-20 16:22:03 (Show Source): You can put this solution on YOUR website!How many litres of a 30% acid solution should be added to 20 litres of 60% acid solution in order to obtain a 50% acid solution? : Let x = amt of 30% solution required : Write a decimal equiv, mixture equation .30x + .60(20) = .50(x+20) .30x + 12 = .5x + 10 12 - 10 = .5x - .3x 2 = .2x x = x = 10 liters of 30% stuff required
 Travel_Word_Problems/472384: i forgot how to solve equations as so: an airplane is traveling a speed of 250 m/h. its destination is 50 miles away. how long will it take to get the airplane to its destination? i do not know how to set this up to be solved.1 solutions Answer 323923 by ankor@dixie-net.com(15667)   on 2011-07-20 14:58:25 (Show Source): You can put this solution on YOUR website!an airplane is traveling a speed of 250 m/h. its destination is 50 miles away. how long will it take to get the airplane to its destination? : Learn the relationships between speed (s), distance, (d), and time (t) d = s * t s = t = : In this problem, you are finding t
 Equations/472405: Multiply using FOIL (x+2) (x-5)1 solutions Answer 323920 by ankor@dixie-net.com(15667)   on 2011-07-20 14:47:00 (Show Source): You can put this solution on YOUR website!Multiply using FOIL (x+2) (x-5) : First: x * x = x^2 Outer: x * -5 = -5x Inner: 2 * x = 2x Last: 2 * -5 = -10 Put it altogether: x^2 - 5x + 2x - 10 Combine like terms x^2 - 3x - 10 : That's how you "FOIL", pretty easy, right?
 Geometry_Word_Problems/472396: A square poster has sides measuring 2 feet less than the sides of a square sign. If the difference between their areas is 44 aquare feet, find the lenghts of the sides of the poster and sign.1 solutions Answer 323917 by ankor@dixie-net.com(15667)   on 2011-07-20 14:41:22 (Show Source): You can put this solution on YOUR website!A square poster has sides measuring 2 feet less than the sides of a square sign. If the difference between their areas is 44 square feet, find the lengths of the sides of the poster and sign. : Let x = the length of the side of the sign then (x-2) = the length of the side of the poster : x^2 = the area of the sign and (x-2)^2 = the area of the poster : Sign area - poster area = 44 sq/ft x^2 - (x-2)^2 = 44 : FOIL (x-2)(x-2) x^2 - (x^2 - 4x + 4) = 44 : Removing the brackets changes the signs x^2 - x^2 + 4x - 4 = 44 4x = 44 + 4 4x = 48 x = x = 12 ft the side of the sign and 12-2 = 10 ft the side of the poster : : Check: 12^2 - 10^2 = 44
 Volume/472269: A rectangular beam of timber is 16 meters long, 80 centimeters wide and 50 centimeters deep. If a piece containing 2 cubic meters cut from the beam perpendicular to its length, what length would be left?1 solutions Answer 323877 by ankor@dixie-net.com(15667)   on 2011-07-20 12:33:34 (Show Source): You can put this solution on YOUR website!A rectangular beam of timber is 16 meters long, 80 centimeters wide and 50 centimeters deep. If a piece containing 2 cubic meters cut from the beam perpendicular to its length, what length would be left? : Convert 80 cm to .8 meters Convert 50 cm to .5 meters : Let p = length of the piece cut from the beam : The volume of the cut piece p * .5 * .8 = 2 .4p = 2 p = p = 5 meters long then 16 - 5 = 11 meters left
 Reduction-of-unit-multipliers/471960: Sam spends \$10 more than half of his money. If this amount of money is the same as \$60 more than one-seventh of his money, how much money did Sam have to begin with?1 solutions Answer 323733 by ankor@dixie-net.com(15667)   on 2011-07-19 21:37:11 (Show Source): You can put this solution on YOUR website!Sam spends \$10 more than half of his money. If this amount of money is the same as \$60 more than one-seventh of his money, how much money did Sam have to begin with? : Let x = original amt : x - (.5x+10) = x + 60 x - .5x - 10 = x + 60 .5x = x + 60 + 10 .5x = x + 70 multiply by 7, results: 7(.5x) = x + 7(70) 3.5x - x = 490 2.5x = 490 x = x = \$196, his original amt : : Check this in the given statement; half 196 = 98 196 - (98+10) = (196) + 60 196 - 108 = 28 + 60 88 = 88
 Geometry_Word_Problems/471952: if the hypotenuse of a right triangle is 37 kilometers and one of the legs is 35 kilometers,what is the area of the triangle1 solutions Answer 323729 by ankor@dixie-net.com(15667)   on 2011-07-19 21:23:20 (Show Source): You can put this solution on YOUR website!if the hypotenuse of a right triangle is 37 kilometers and one of the legs is 35 kilometers, what is the area of the triangle : Let a = the unknown leg of the right triangle, then we have a^2 + 35^2 = 37^2 a^2 + 1225 = 1369 a^2 = 1369 - 1225 a^2 = 144 a = a = 12 km is the other leg : Find the area A = *12*35 A = 210 sq/km
 Numbers_Word_Problems/472097: a number is twelve less than five times another number.their sum is one hundred sixty-two. what are the numbers1 solutions Answer 323726 by ankor@dixie-net.com(15667)   on 2011-07-19 21:15:49 (Show Source): You can put this solution on YOUR website!a number is twelve less than five times another number. their sum is one hundred sixty-two. what are the numbers : Let x = "a number" Let y = "another number" : Write an equation for each statement. : "a number is twelve less than five times another number." x = 5y - 12 : "their sum is one hundred sixty-two." x + y = 162 replace x with (5y-12) (5y-12) + y = 162 5y + y = 162 + 12 6y = 174 y = y = 29 : Find x x = 5(29) - 12 x = 145 - 12 x = 133 : : Check 133 + 29 = 162
 Rate-of-work-word-problems/471995: if you work 25 1/2 hours get paid 7.5 an hour how much is it1 solutions Answer 323725 by ankor@dixie-net.com(15667)   on 2011-07-19 21:08:02 (Show Source): You can put this solution on YOUR website!Do this: 25.5 * 7.5
 test/472108: Factor completely 2x(exponent 3)+24x(exponent 2)+40x1 solutions Answer 323719 by ankor@dixie-net.com(15667)   on 2011-07-19 20:58:23 (Show Source): You can put this solution on YOUR website!Factor completely 2x^3 + 24x^2 + 40x Factor out 2x 2x(x^2 + 12x + 20) The quadratic will factor to 2x(x+10)(x+2)
 Average/471760: If the average of two numbers is 73, and if one of the numbers is 59, then what is the other number? Please show all of your work A=a+b 21 solutions Answer 323714 by ankor@dixie-net.com(15667)   on 2011-07-19 20:53:13 (Show Source): You can put this solution on YOUR website!If the average of two numbers is 73, and if one of the numbers is 59, then what is the other number? Please show all of your work ; Let x = the other number = 73 multiply both sides by 2 x + 59 = 2(73) x + 59 = 146 x = 146 - 59 x = 87 is the other number
 Percentage-and-ratio-word-problems/471813: darren can paint 4 fence sections in 2.3 hours. how long will it take him to paint 64 sections? 1 solutions Answer 323670 by ankor@dixie-net.com(15667)   on 2011-07-19 18:44:28 (Show Source): You can put this solution on YOUR website!darren can paint 4 fence sections in 2.3 hours. how long will it take him to paint 64 sections? : 64() = 36.8 hrs
 Triangles/471778: If in a right triangle the side adjacent to 60 deg is 6 cm. long, the hypotenuse is 1 solutions Answer 323657 by ankor@dixie-net.com(15667)   on 2011-07-19 17:32:47 (Show Source): You can put this solution on YOUR website!If in a right triangle the side adjacent to 60 deg is 6 cm. long, the hypotenuse is " Use the cos(60), : cos(60) = .5 = .5h = 6 h = 12
 Equations/471804: A projectile is fired from a cliff 100 feet above the water at an inclination of 45° to the horizontal, with a muzzle velocity of 170 feet per second. The height h of the projectile above the water is given by where x is the horizontal distance of the projectile from the base of the cliff. How far from the base of the cliff is the height of the projectile a maximum? A. 225.78 ft B. 451.56 ft C. 325.78 ft D. 777.34 ft 1 solutions Answer 323636 by ankor@dixie-net.com(15667)   on 2011-07-19 15:57:46 (Show Source): You can put this solution on YOUR website!A projectile is fired from a cliff 100 feet above the water at an inclination of 45° to the horizontal, with a muzzle velocity of 170 feet per second. The height h of the projectile above the water is given by where x is the horizontal distance of the projectile from the base of the cliff. How far from the base of the cliff is the height of the projectile a maximum? : Convert the coefficient of x^2 to a more manageable value : = -.001107, so we have h(x) = -.001107x^2 + x + 100 : find the axis of symmetry, x = -b/(2a), in this equation a=-.001107, b=1 x = x = +451.6 ft from the base of the cliff, it will be at max height
 Mixture_Word_Problems/471866: Sally has a glass that is 1/3 filled with syrup. Bob has a glass that is 1/4 filled with syrup but Bob's glass holds twice as much as Sally's. If they were to fill the rest of their glasses with milk, then mix them together, what part of the combine mixture would be syrup. Please let me know the process of solving this problem.1 solutions Answer 323597 by ankor@dixie-net.com(15667)   on 2011-07-19 12:57:28 (Show Source): You can put this solution on YOUR website!Sally has a glass that is 1/3 filled with syrup. Bob has a glass that is 1/4 filled with syrup but Bob's glass holds twice as much as Sally's. If they were to fill the rest of their glasses with milk, then mix them together, what part of the combine mixture would be syrup. : let x = amt to fill Sally's glass and 2x = amt to fill Bob's glass then total amt when mixed together = 3x : Sally's syrup = x Bob's syrup = (2x) = x = x : x + x = x + x = x; amt of syrup when mixed together Find what part 3x is x? : The x's cancel so we have: = * = of the total mixture is syrup
 Miscellaneous_Word_Problems/471557: The bacteria in a 9-liter container doubble every 4 minutes. After 54 minutes the container is full. How long did it take to fill a quarter of the container?1 solutions Answer 323432 by ankor@dixie-net.com(15667)   on 2011-07-18 16:24:30 (Show Source): You can put this solution on YOUR website!The bacteria in a 9-liter container double every 4 minutes. After 54 minutes the container is full. How long did it take to fill a quarter of the container? : You can reason this out. If it takes 4 min to double, then it would be half full at 50 min, then 1/4 full in 46 min : You can confirm this with numbers : Find the number of bacteria when full 2^(54/4) = 11585.24 * 11585.24 = 2896.31 let = no. minutes to be 1/4 full 2^(t/4) = 2896.31 using logs = = 11.5 t = 11.5 * 4 t = 46 min to be 1/4 full
 Travel_Word_Problems/471491: A motorboat maintained a constant speed of 11 miles per hour relative to water in Goin 30 miles upstream and then returning. The total time for the trip was 5.5 hours. Use this information to find the speed of the current 1 solutions Answer 323421 by ankor@dixie-net.com(15667)   on 2011-07-18 15:45:37 (Show Source): You can put this solution on YOUR website!A motorboat maintained a constant speed of 11 miles per hour relative to water in Going 30 miles upstream and then returning. The total time for the trip was 5.5 hours. : Let c = speed of the current then (11+c) = speed downstream relative to land and (11-c) = speed upstream relative to the land : Write a time equation: time = dist/speed : time upstream + time downstream = 5.5 hrs + = 5.5 : Multiply by (11-c)(11+c), results: 30(11+c) + 30(11-c) = 5.5(11+c)(11-c) : 330 + 30c + 330 - 30c = 5.5(121 - 11c + 11c - c^2) : 660 = 5.5(121 - c^2) : 660 = 665.5 - 5.5c^2 : 5.5c^2 = 665.5 - 660 : 5.5c^2 = 5.5 Divide both sides by 5.5 c^2 = 1 c = 1 mph is the current : : See if this is true; find the times both ways downstream: 30/12 = 2.5 hrs up-stream: 30/10 = 3.0 hrs ---------------- total time: 5.5 hrs
 Equations/471527: I need help/refresher on how to solve for x 1/12 - x-1/12 = - /4 thanks for your help Chase1 solutions Answer 323419 by ankor@dixie-net.com(15667)   on 2011-07-18 15:28:44 (Show Source): You can put this solution on YOUR website!Assume the problem is: - = multiply by the common denominator 12* - 12* = 12* Cancel the denominators 1 - (x-1) = -3 Removing the bracket changes the signs to: 1 - x + 1 = -3 -x + 1 + 1 = -3 -x + 2 = -3 subtract 2 from both sides -x = -3 -2 -x = -5 multiply both sides by -1 x = 5 : : See if that flies in the original equation - = - =
 Rectangles/471529: If a garden box is x by x square feet and the area is three times the perimeter what is the value for x? a=24 feet b=12 feet c=6 feet1 solutions Answer 323411 by ankor@dixie-net.com(15667)   on 2011-07-18 15:08:02 (Show Source): You can put this solution on YOUR website!If a garden box is x by x square feet and the area is three times the perimeter what is the value for x? : The area: x^2 the perimeter 4x : 3x^2 = 4x Divide both sides by x 3x = 4 x = x = 1 ft : : Check this: Find 3 time the area: 3(1.33^2) ~ 5.3 Find the perimeter: 4(1.33) ~ 5.3 : He sorry that I got this backwards, it should be x^2 = 3(4x) x^2 = 12x Divide by x x = 12
 Quadratic_Equations/471488: Please provide detailed steps to solving the following word problem: A ball is thrown upward with an intial velocity of 14 meters per second (mps) from a cliff that is 70 meters high. The height of the ball is given by the quadratic equation h = -4.9t^2 + 14t + 90 where h is in meters and t is the time in seconds since the ball was thrown. Find the time that the ball will be 20 meters from the ground...rounded to the nearest tenth of a second1 solutions Answer 323380 by ankor@dixie-net.com(15667)   on 2011-07-18 12:48:36 (Show Source): You can put this solution on YOUR website!A ball is thrown upward with an initial velocity of 14 meters per second (mps) from a cliff that is 70 meters high. The height of the ball is given by the quadratic equation h = -4.9t^2 + 14t + 90 where h is in meters and t is the time in seconds since the ball was thrown. Find the time that the ball will be 20 meters from the ground...rounded to the nearest tenth of a second : Just take the given equation, replace h with 20 and you have: -4.9t^2 + 14t + 90 = 20 arrange it into a quadratic equation -4.9t^2 + 14t + 90 - 20 = 0 -4.9t^2 + 14t + 70 = 0 Use the quadratic formula to find t In this equation x=t; a=-4.9; b=14; c=70 : : : Two solutions t = t = -2.6, obviously this is not the solution and t = t = 5.47 ~ 5.5 seconds it will be at 20 meter : : You can prove this to yourself, substitute 5.47 for t in the original equation and see that h ~ 20m
 Age_Word_Problems/471453: Josh is half as old as his brother Luke. Nicola, who is exactly half-way between her two brothers, is 18. How old is Josh?1 solutions Answer 323355 by ankor@dixie-net.com(15667)   on 2011-07-18 11:05:01 (Show Source): You can put this solution on YOUR website!Josh is half as old as his brother Luke. Nicola, who is exactly half-way between her two brothers, is 18. How old is Josh? : Let j = J's age then .5j = Bro's age and .5j = the difference between them : Bro's age + half of the difference between them is Nicola's age .5j + .5(.5j) = 18 .5j + .25j = 18 .75j = 18 j = j = 24 yrs is Josh's age : : Check: Bro's age = 12 yrs, Nicola's age, 18, is halfway between 12 and 24
 Circles/471431: the cone is half filled with water find the volume of water present in the cone given(use pi as 22over7 the height is 10 for the whole cone and the radius is 7 but for the half one the radius 3 please show the working1 solutions Answer 323332 by ankor@dixie-net.com(15667)   on 2011-07-18 08:42:07 (Show Source): You can put this solution on YOUR website!the cone is half filled with water find the volume of water present in the cone given(use pi as 22over7 the height is 10 for the whole cone and the radius is 7 but for the half one the radius 3 please show the working : The volume of a cone formula: V = : Assuming that half full means the height of the water is 5, find vol of the water V = ** V = 47.143 cu/units
 Quadratic_Equations/471331: an artifact was found and tested for its carbon-14 content. If 81% of the original carbon-14 was still present, what is it probable age(to the nearest 100yrs)? use that carbon-14 has a half-life of 5730 yrs.1 solutions Answer 323268 by ankor@dixie-net.com(15667)   on 2011-07-17 20:58:56 (Show Source): You can put this solution on YOUR website!an artifact was found and tested for its carbon-14 content. If 81% of the original carbon-14 was still present, what is it probable age(to the nearest 100yrs)? use that carbon-14 has a half-life of 5730 yrs. : The half life formula: A = Ao*2^(-t/h) Where A = resulting amt after t yrs Ao = initial amt t = time in yrs h = half-life of substance : When we are dealing with percent we can use the initial amt of 100 : 100*2^(-t/5730) = 81 2^(-t/5730) = 2^(-t/5730) = .81 find the nat log of both sides ln(2^(-t/5730)) = ln(81) log equiv of exponents ln(2) = ln(81) = = -.304 multiply both sides by -5730, results t = 1,742 yrs
 Miscellaneous_Word_Problems/471335: Patricia Burgess knows that at some point during the calender year her basic monthly telephone rate increased from \$17.10 to \$18.40. If she paid a total of \$207.80 for basic telephone service for the calender year, in what month did the rate increase take effect1 solutions Answer 323256 by ankor@dixie-net.com(15667)   on 2011-07-17 20:16:56 (Show Source): You can put this solution on YOUR website!during the calender year her basic monthly telephone rate increased from \$17.10 to \$18.40. If she paid a total of \$207.80 for basic telephone service for the calender year, in what month did the rate increase take effect : Let m = no. months she paid \$17.10 then (12-m) = no. of months she paid \$18.40 : 17.10m + 18.40(12-m) = 207.80 17.10m + 220.80 - 18.40m = 207.80 17.10m - 18.40m = 207.80 - 220.80 -1.30m = -13 m = m = +10 months at the lower rate, then the increase took effect in the 11th month (Nov) : : see if that's true 10(17.10) + 2(18.40) = 171.00 + 36.80 = 207.80
 Inequalities/471286: Milly is two thirds as old as Marcia. Four years from now she will be at most five sevenths as old as Marcia. At least how old is Milly? This question needs to be resolved in inequalities.1 solutions Answer 323254 by ankor@dixie-net.com(15667)   on 2011-07-17 20:05:58 (Show Source): You can put this solution on YOUR website!Milly is two thirds as old as Marcia. Four years from now she will be at most five sevenths as old as Marcia. At least how old is Milly? : let mi = Milly's present age let ma = Marcia's present age : Write an equation for each statement: : "Milly is two thirds as old as Marcia." mi = ma : " Four years from now she will be at most five sevenths as old as Marcia. mi + 4 =< (ma+4) multiply both sides by 7 7(mi+4) =< 5(ma+4) 7mi + 28 =< 5ma + 20 7mi =< 5ma + 20 - 28 7mi =< 5ma - 8 Replace mi with ma 7(ma) =< 5ma - 8 multiply both sides by 3 14ma =< 15ma - 24 14 ma - 15ma =< - 24 -1ma =< -24 multiply both sides by -1, this reverses the inequality sign ma => 24 then mi => *24 mi => 16
 Travel_Word_Problems/471293: three travelers meet whenever they are all in los angeles at the same time. One traveler visits every 24 days, the second visits every 36 days. and the third visits every 54 days. if they meet today, how many days will pass before they meet again?1 solutions Answer 323232 by ankor@dixie-net.com(15667)   on 2011-07-17 18:47:26 (Show Source): You can put this solution on YOUR website!three travelers meet whenever they are all in los angeles at the same time. One traveler visits every 24 days, the second visits every 36 days. and the third visits every 54 days. if they meet today, how many days will pass before they meet again? : Prime factor the three intervals 24: 2 * 2 * 2 * 3 36: 2 * 2 * 3 * 3 54: 2 * 3 * 3 * 3 : LCM: 2 * 2 * 2 * 3 * 3 * 3 = 216 days