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 Numeric_Fractions/628314: 1500 is divided into three parts , 1/2 of the first part is same as 1/3rd of the second and 3/5th of third. find each part 1 solutions Answer 395575 by ankor@dixie-net.com(15747)   on 2012-07-14 12:59:15 (Show Source): You can put this solution on YOUR website!1500 is divided into three parts, 1/2 of the first part is same as 1/3rd of the second and 3/5th of third. find each part : "1500 is divided into three parts," a + b + c = 1500 : "1/2 of the first part is same as 1/3rd of the second" a = b multiply by 3 a = b : "and 3/5th of third. find each part" a = c multiply by (5/3) a = c : replace b and c in the total equation a + a + a = 1500 multiply by 6, results 6a + 3(3a) + 5a = 6(1500) 6a + 9a + 5a = 9000 20a = 9000 a = 9000/20 a = 450 is the 1st part then b = *450 b = 675 is the 2nd part and c = *450 c = 375 is the 3rd part : : See if that adds up: 450 + 675 + 375 = 1500
 Travel_Word_Problems/628312: An automobile car traveled 200 miles and at same time a track can travel 150 miles .If the automobile travels at the average speed of 15 miles per hour faster than the track then . Find their average rate?1 solutions Answer 395565 by ankor@dixie-net.com(15747)   on 2012-07-14 11:16:08 (Show Source): You can put this solution on YOUR website!An automobile car traveled 200 miles and at same time a truck can travel 150 miles . If the automobile travels at the average speed of 15 miles per hour faster than the truck then . Find their average rate? : Let s = speed of the truck then (s+15) = speed of the car ; Write a time equation: time = dist/speed : truck time = car time = Cross multiply 150(s+15) = 200s 150s = 2250 = 200s 2250 = 200s - 150s 2250 = 50s s = 2250/50 s = 45 mph is the speed of the truck then 45 + 15 = 60 mph is the speed of the car : : Confirm this by finding the time of each, they should be equal 150/45 = 3.33 hrs 200/60 = 3.33 hrs
 Numbers_Word_Problems/628279: nine times a two digit number is the same as twice the number obtained on interchanging the digits of the number.If one digit of the number exceeds the other by 7,find the number. 1 solutions Answer 395517 by ankor@dixie-net.com(15747)   on 2012-07-13 21:35:12 (Show Source): You can put this solution on YOUR website!let x = the 10's digit let y = the units then 10x+y = "the number" and 10y+x = "the number reversed : write an equation for each statement : "nine times a two digit number is the same as twice the number obtained on interchanging the digits of the number." 9(10x+y) = 2(10y+x) 90x + 9y = 20y + 2x 90x - 2x = 20y - 9y 88x = 11y simplify, divide by 11 8x = y ; "If one digit of the number exceeds the other by 7," y = x + 7 (y has to be the larger number) replace y with 8x 8x = x + 7 8x - x = 7 7x = 7 x = 1 then y = 8 : 18 is the original number : : Check this in the 1st statement 9(18) = 2(81)
 Unit_Conversion_Word_Problems/628256: a car travels 255 miles in 3 hours and 45 minutes. how many miles does it travel per hour?1 solutions Answer 395514 by ankor@dixie-net.com(15747)   on 2012-07-13 21:14:33 (Show Source): You can put this solution on YOUR website!a car travels 255 miles in 3 hours and 45 minutes. how many miles does it travel per hour? : Change time to 3.75 hrs : speed = dist/time : s = s = 68 mph
 test/628205: A rectangular garden is 60 ft by 80 ft. Part of the garden is torn up to install a sidewalk of uniform width around the garden. The new area of the garden is one sixth of the old area. How wide is the sidewalk? 60-x, 80-x1 solutions Answer 395469 by ankor@dixie-net.com(15747)   on 2012-07-13 16:19:52 (Show Source): You can put this solution on YOUR website!A rectangular garden is 60 ft by 80 ft. Part of the garden is torn up to install a sidewalk of uniform width around the garden. The new area of the garden is one sixth of the old area. How wide is the sidewalk? : Let x = the width of the walk : The new dimensions of the garden will be (60-2x) by (80-2x) : Find the original area: 60*80 = 4800 sq/ft Find the new area: *4800 = 800 sq/ft : (60-2x)*(80-2x) = 800 FOIL 4800 - 120x - 160x + 4x^2 = 800 Combine on the left as a quadratic equation 4x^2 - 280x + 4800 - 800 = 0 4x^2 - 280x + 4000 = 0 simplify divide by 4 x^2 - 70x + 1000 = 0 Factors to (x-20)(x-50) = 0 Two solutions x = 50, not reasonable and x = 20 ft is the width of the walk : : Check this with the new dimensions (2x = 40): (80-40)*(60-40) = 800 sq/ft
 Travel_Word_Problems/628186: Train A travels at 90 miles per hour and covers 360 miles. Train B covers the same distance but travels at 60 miles per hour. How much longer does it take Train B than Train A to cover that distance?1 solutions Answer 395466 by ankor@dixie-net.com(15747)   on 2012-07-13 16:08:19 (Show Source): You can put this solution on YOUR website!Train A travels at 90 miles per hour and covers 360 miles. Train B covers the same distance but travels at 60 miles per hour. How much longer does it take Train B than Train A to cover that distance? : Write a time equation, t = -
 Square-cubic-other-roots/628207: How do I factor a radicand to the perfect fourth power? I have the problem. 4√486x^12y^14. I know that it becomes 4√81*6*x^12y^14 and the answer is 3x^3y^34√6y^2. I am having trouble understanding how 486 became 81 and then 3x. your help would be greatly appreciated. 1 solutions Answer 395462 by ankor@dixie-net.com(15747)   on 2012-07-13 15:48:33 (Show Source): You can put this solution on YOUR website!the problem. factor in a manner that will will reveal the perfect 4th power values 4th power of 3 is 81 and is also a factor of 486, going into that 6 times : extract the 4th root of the perfect 4ths and you have 3*x*x*x*y*y* which is
 Geometry_Word_Problems/628217: If I can fill a 20 gallon sink 512 times, how many times can I fill a 30 gallon sink?1 solutions Answer 395459 by ankor@dixie-net.com(15747)   on 2012-07-13 15:34:25 (Show Source): You can put this solution on YOUR website! = 341 times
 Square-cubic-other-roots/628215: how does the original question is the first part but the second part is the answer. i just cant figure out how to get from one part to the other1 solutions Answer 395458 by ankor@dixie-net.com(15747)   on 2012-07-13 15:30:37 (Show Source): You can put this solution on YOUR website! It's quite apparent if you factor this Cancel out (x-1)'s and see what you have
 Travel_Word_Problems/628203: Two trucks left two towns A and B at the same time, and each was headed to the other town at a constant speed, passing each other at point C. The truck from town B completed the journey from C to A in 20 minutes. The truck from A completed the journey from A to C in 45 minutes, while maintaining its steady speed of 45 km/h. Find the speed of the truck from B in km/h, assuming that it maintains a constant speed throughout.1 solutions Answer 395457 by ankor@dixie-net.com(15747)   on 2012-07-13 15:25:39 (Show Source): You can put this solution on YOUR website!Two trucks left two towns A and B at the same time, and each was headed to the other town at a constant speed, passing each other at point C. The truck from town B completed the journey from C to A in 20 minutes. The truck from A completed the journey from A to C in 45 minutes, while maintaining its steady speed of 45 km/h. Find the speed of the truck from B in km/h, assuming that it maintains a constant speed throughout. : A <--------<20min<--------C----------------< B; truck from B A >-------->45min>-------C-----------------> B: truck from A (at 45km/h) : Change 20 min to .33 hrs Change 45 min to .75 hrs : Since truck from A completed the distance from A to C in 45 min at 45 km/h, dist from A to C: .75(45) = 33.75 km : Find the speed of truck from B, which traveled from C to A in 20 min: S = = 101.25 km/hr
 Travel_Word_Problems/628190: If Mark is travelling South at 10 miles per hour for 45 minutes, and Sally is travelling North at 5 miles per hour for 30 minutes, and they meet after one hour, how far apart where they when they began1 solutions Answer 395444 by ankor@dixie-net.com(15747)   on 2012-07-13 13:55:32 (Show Source): You can put this solution on YOUR website!If Mark is traveling South at 10 miles per hour for 45 minutes, and Sally is traveling North at 5 miles per hour for 30 minutes, and they meet after one hour, how far apart were they when they began? : The distance they were apart will equal the total distance they traveled. : Write a distance equation; d = speed * time : Change 45 min to .75 hrs, and 30 min to .5 hrs : d = 10(.75) + 5(.5) d = 7.5 + 2.5 d = 10 mi apart : Not sure how "they meet after one hour" fits into this
 Trigonometry-basics/628147: from an h=63 feet observation tower on the coast, a coast guard sights a boat. the angle of depression is 4 degrees. how far is the boat from the shore line?1 solutions Answer 395439 by ankor@dixie-net.com(15747)   on 2012-07-13 13:36:22 (Show Source): You can put this solution on YOUR website!from an h=63 feet observation tower on the coast, a coast guard sights a boat. the angle of depression is 4 degrees. how far is the boat from the shore line? : The interior angle of the right triangle formed by tower, the boat and the shore line: 90 - 4 = 86 degrees : The tangent can be used here, side opposite/side adjacent Let s = distance from the shore to the boat (side opposite 86 degrees) : tan(86) = s = 63 * tan(86) s = 63 * 14.3 s = 900.94 ft from the shore to the boat
 Miscellaneous_Word_Problems/628134: mike and dave are roommates. one day mike wakes up and goes for his morning run. He runs 8 miles per hour. an hour later, dave leaves ro his morning bike ride traveling the same route as mike. Dave bikes 20 miles per hour. How log will mike have been running when dave catches him?1 solutions Answer 395416 by ankor@dixie-net.com(15747)   on 2012-07-13 10:10:22 (Show Source): You can put this solution on YOUR website!Mike runs 8 miles per hour. An hour later, Dave leaves for his morning bike ride traveling the same route as mike. Dave bikes 20 miles per hour. How long will mike have been running when Dave catches him? : Let t = Mike's running time then (t-1) = Dave's travel time (left an hr after Mike) : When Dave catches Mike, they will have traveled the same distance. Write a distance equation: dist = speed * time : 20(t-1) = 8t 20t - 20 = 8t 20t - 8t = 20 12t = 20 t = 20/12 t = 1 hrs which would be 1 hr 40 min, Mike's running time. : : Check this by finding the dist each traveled, should be equal Mike: 1.67 * 8 = 13.33 miles Dave: .67 * 20 = 13.33 miles
 Rate-of-work-word-problems/628130: I am trying to work this word problem and cannot figure out where to start. Thanks for your assistance. John works two part-time jobs for a total of 25 hours per week. Job A pays \$7.50 per hour and Job B pays \$8.40 per hour. How many hours did he work at each job if he made \$200.10 this week? 1 solutions Answer 395405 by ankor@dixie-net.com(15747)   on 2012-07-13 09:23:28 (Show Source): You can put this solution on YOUR website!John works two part-time jobs for a total of 25 hours per week. Job A pays \$7.50 per hour and Job B pays \$8.40 per hour. How many hours did he work at each job if he made \$200.10 this week? : Let a = no. of hrs worked at job A Let b = no. of hrs worked at job B : Write an equation for each statement; : "John works two part-time jobs for a total of 25 hours per week." a + b = 25 a = (25-b); we can use this form for substitution ; "Job A pays \$7.50 per hour and Job B pays \$8.40 per hour.he made \$200.10" 7.50a + 8.40b = 200.10 replace a with (25-b) 7.50(25-b) + 8.40b = 200.10 187.50 - 7.50b + 8.40b = 200.10 -7.50b + 8.40b = 200.10 - 187.50 .90b = 12.60 b = 12.60/.9 b = 14 hrs on job B : I'll let you find job A, ensure the \$ add up 200.10
 Miscellaneous_Word_Problems/628073: Twin brothers, person A and person B, can mow their grandparents lawn together in 42 minutes. Person B takes 13 minutes more than person A. How long does it take each person to mow alone?1 solutions Answer 395356 by ankor@dixie-net.com(15747)   on 2012-07-12 22:02:26 (Show Source): You can put this solution on YOUR website!Twin brothers, person A and person B, can mow their grandparents lawn together in 42 minutes. Person B takes 13 minutes more than person A. How long does it take each person to mow alone? : let t = time required by A to mow it alone then (t+13) = time required by B Let the completed job = 1 (a mowed lawn) : A shared work equation : + = 1 multiply by x(x+13), resulting in eliminating the denominators, 42(x+13) + 42x = x(x+13) : 42x + 546 + 42x = x^2 + 13x 84x + 546 = x^2 + 13x 0 = x^2 + 13x - 84x - 546 A quadratic equation x^2 - 71x - 546 = 0 You can use the quadratic formula here, but this will factor (x+7)(x-78) = 0 the positive solution x = 78 minutes, A alone then 78+13 = 91 min. B alone : : See if that works out on a calc: 42/78 + 42/91 = 1
 Exponents/628008: Use algebraic procedures to find the exact solution(s) of the equation. (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.) e^(x + 3) = 22 x=?1 solutions Answer 395354 by ankor@dixie-net.com(15747)   on 2012-07-12 21:49:43 (Show Source): You can put this solution on YOUR website!e^(x + 3) = 22 Find the nat log of each side ln(e^x+3)) = ln(22) log equiv of exponents (x+3)ln(e) = ln(22) Find the log, ln of e is 1 so we have x + 3 = 3.09104 x = 3.09104 - 3 x = .09104 : : Check this on you calc enter e^(.09104+3) results: 21.99999 ~ 22
 Travel_Word_Problems/627844: A train takes 2 hours to reach station b from station a, and then 3 hours to return from station b to station a. The distance between the stations is 200 km. Find the (a) average speed and (b) average velocity of the train. please find the velocity1 solutions Answer 395341 by ankor@dixie-net.com(15747)   on 2012-07-12 20:53:54 (Show Source): You can put this solution on YOUR website!A train takes 2 hours to reach station b from station a, and then 3 hours to return from station b to station a. The distance between the stations is 200 km. Find the (a) average speed let a = average speed, it took 5 hrs to travel 400 km a = a = 80 km/hr : (b) average velocity of the train. Velocity involves direction and displacement Since it ended up in the same place it started (A); velocity is 0
 Travel_Word_Problems/627846: by how much is a car exceeding the speed limit of 100km/hr if it travels at 180 kms in 1.5 hours1 solutions Answer 395335 by ankor@dixie-net.com(15747)   on 2012-07-12 20:34:17 (Show Source): You can put this solution on YOUR website!by how much is a car exceeding the speed limit of 100km/hr if it travels at 180 kms in 1.5 hours : Find the actual speed; speed = dist/time = 120 km/h : You decide how much over the speed limit that is.
 Distributive-associative-commutative-properties/627882: REplace A with proper expression where the fractions are equivalent: 7/a+5=7a-35/A. I am not sure how to go about solving these kind of problems. Any help would be appreciated. Thank you1 solutions Answer 395334 by ankor@dixie-net.com(15747)   on 2012-07-12 20:29:24 (Show Source): You can put this solution on YOUR website!REplace A with proper expression where the fractions are equivalent: : = factor out 7 in the 2nd numerator = divide both sides by 7, results: = Cross multiply A = (a+5)(a-5) A = a^2 - 25 Equiv: =
 test/628006: a will states that 3/5 of an estate is to be divided among relatives. Of the remaining, 1/4 goes to charity. How much goes to charity1 solutions Answer 395289 by ankor@dixie-net.com(15747)   on 2012-07-12 17:10:39 (Show Source): You can put this solution on YOUR website!a will states that 3/5 of an estate is to be divided among relatives. Of the remaining, 1/4 goes to charity. How much goes to charity : Remaining will be 2/5 : * = = to charity
 Square-cubic-other-roots/627913: (x-22)^2 Please solve using square root property Thank you1 solutions Answer 395288 by ankor@dixie-net.com(15747)   on 2012-07-12 17:06:27 (Show Source): You can put this solution on YOUR website!(x-22)^2 Please solve using square root property This is not an equation, just an expression, did you mean? (x-22)^2 = 0 (x-22)(x-22) = 0 solution x = 22
 Functions/628024: I can not seem to grasp how to find the answers for problems like this: Multiply and simplify by factoring. I think what I am having the problem understanding is the "perfect square" factors. √12* √150 Thanks for all your help.1 solutions Answer 395285 by ankor@dixie-net.com(15747)   on 2012-07-12 16:53:38 (Show Source): You can put this solution on YOUR website!√12* √150 : Factor inside the radicals to reveal perfect squares * Extract the square root of those squares * Multiply now factor to reveal a perfect square again, extract the square root of 9 = =
 Travel_Word_Problems/627892: Please help me with this word problem. Thank you very much! A turkey takes 6.25 hours to cook and instructions said 15 minutes per ound, how many ounds was the turkey?1 solutions Answer 395279 by ankor@dixie-net.com(15747)   on 2012-07-12 16:08:39 (Show Source): You can put this solution on YOUR website!A turkey takes 6.25 hours to cook and instructions said 15 minutes per pound, how many pounds was the turkey? : change 15 min to hrs: 15/60 = .25 lb = 25 lb