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 Travel_Word_Problems/522689: David is traveling to the airport to catch a flight, if he travels at the speed of 30 mph, he is late by 13 minutes. If he travels at the speed of 40 mph, he will arrive 7 minutes earlier than the scheduled departure time of the flight. What is the distance to the airport (in miles)?1 solutions Answer 346973 by ankor@dixie-net.com(15746)   on 2011-10-28 10:58:20 (Show Source): You can put this solution on YOUR website!David is traveling to the airport to catch a flight, if he travels at the speed of 30 mph, he is late by 13 minutes. If he travels at the speed of 40 mph, he will arrive 7 minutes earlier than the scheduled departure time of the flight. What is the distance to the airport (in miles)? : Let d = distance to airport Let s = speed required to arrive on time then = the ideal time to the airport : Write a time equation for each scenario : - = ; late - + = ; early --------------------------------------- addition, eliminates d/s - + 0 = Clear denominators, multiply by 120, results: 4d - 3d = 2(20) d = 40 mi to the airport : : See if this works; find s - = ; mult by 60s, results 2s(40) - 60(40) = 13s 80s - 2400 = 13s 80s - 13s = 240 67s = 2400 s = s = 35.82 mph the ideal speed : Check solution in the late equation - = 1.3333 - 1.1167 = .2166 hr which is 13 min
 Travel_Word_Problems/522669: Please can you help me with the workings for this word problem as I am unable to do so: A man is rowing a boat up a river and his hat falls in the water. He doesn't notice and keeps rowing for ten minutes before he realises his hat is gone. He turns his boat and rows after it. He rows and retieves his hat which has floated three kilometres downstream from the where it fell in the water. How fast was the river flowing?1 solutions Answer 346968 by ankor@dixie-net.com(15746)   on 2011-10-28 10:00:53 (Show Source): You can put this solution on YOUR website!A man is rowing a boat up a river and his hat falls in the water. He doesn't notice and keeps rowing for ten minutes before he realises his hat is gone. He turns his boat and rows after it. He rows and retieves his hat which has floated three kilometres downstream from the where it fell in the water. How fast was the river flowing? : The boat and the hat are moving with the current at the same rate, therefore if he rowed 10 min away from the hat he would take 10 min to get back to the hat. A total of 20 min. The hat traveled 3 km in 20 min, 1/3 of an hr, therefore: 3 * 3 = 9 km/hr is the flow rate of the river
 Rational-functions/522705: Please help I just want to make sure that I answered this properly the expression is : -- My LCD is 12 so I mulitply everything by 12 and after I combine like terms I'm left with Thank you for any help in this1 solutions Answer 346961 by ankor@dixie-net.com(15746)   on 2011-10-28 09:24:25 (Show Source): You can put this solution on YOUR website!You're right!
 Divisibility_and_Prime_Numbers/522534: What are the prime factors for these numbers? 90, 24,30,12, 63, 28 1 solutions Answer 346960 by ankor@dixie-net.com(15746)   on 2011-10-28 09:22:51 (Show Source): You can put this solution on YOUR website!What are the prime factors for these numbers? 90, 24,30,12, 63, 28 : 90: 2,3,3,5 24: 2,2,2,3 30: 2,3,5 12: 2,2,3, 63: 3,3,7 28: 2,2,7 : The prime factors of the LCM, 2,2,2,3,3,5,7 = 2520
 Travel_Word_Problems/522311: In a two-boat sailing race, one boat, wind sprite rounds the final buoy and sails straight for the finish line at 12.0 knots. Exactly4 minutes after wind sprite rounds the final buoy, the other boat, and porpoise, reaches that point and heads for the finish line at 12.7 knots. Wind sprite reaches the finish line 49minutes after rounding the last buoy. Who wins the race? 1 solutions Answer 346958 by ankor@dixie-net.com(15746)   on 2011-10-28 09:09:08 (Show Source): You can put this solution on YOUR website!In a two-boat sailing race, one boat, wind sprite rounds the final buoy and sails straight for the finish line at 12.0 knots. Exactly4 minutes after wind sprite rounds the final buoy, the other boat, and porpoise, reaches that point and heads for the finish line at 12.7 knots. Wind sprite reaches the finish line 49minutes after rounding the last buoy. Who wins the race? : The other boat has to complete the race in 4 min less time than the Sprite just to tie, 45 min. Find the time it takes the other boat to cross the finish line Write a time equation, time = dist/speed. : = 46.3 min : The other boat loses by 1.3 min
 Mixture_Word_Problems/522537: Please help me with this question...(How much pure acid shoud be mixed with 2 gallons of an 80% acid solution in order to get a 90% acid solution?) 1 solutions Answer 346904 by ankor@dixie-net.com(15746)   on 2011-10-27 21:40:43 (Show Source): You can put this solution on YOUR website!(How much pure acid should be mixed with 2 gallons of an 80% acid solution in order to get a 90% acid solution?) : Let a = amt of 100% acid required : .80(2) + a = .90(a+2) 1.6 + a = .9a + 1.8 a - .9a = 1.8 - 1.6 .1a = .2 a = .2/.1 a = 2 gal of acid required
 Travel_Word_Problems/522449: Your friend is traveling 3mph faster than you. Together you travel 11 miles in 1 hour. How many miles did each of you travel in that hour?1 solutions Answer 346899 by ankor@dixie-net.com(15746)   on 2011-10-27 21:21:37 (Show Source): You can put this solution on YOUR website!Your friend is traveling 3mph faster than you. Together you travel 11 miles in 1 hour. How many miles did each of you travel in that hour? : Let s = your speed then (s+3) = friend's speed : Write a distance equation, dist = speed * time 1s + 1(s+3) = 11 1s + 1s + 3 = 11 2s = 11 - 3 2s = 8 s = 4 mph, friend: 7 mph Dist the same: you 4 mi, friend 7 mi
 Rate-of-work-word-problems/522450: A roofer requires 10 h to shingle a roof. After the roofer and an apprentice work on a roof for 6 h, the roofer moves on to another job. The apprentice requires 8 more hours to finish the job. How long would it take the apprentice, working alone, to do the job? 1 solutions Answer 346895 by ankor@dixie-net.com(15746)   on 2011-10-27 21:09:52 (Show Source): You can put this solution on YOUR website!A roofer requires 10 h to shingle a roof. After the roofer and an apprentice work on a roof for 6 h, the roofer moves on to another job. The apprentice requires 8 more hours to finish the job. How long would it take the apprentice, working alone, to do the job? : Let a = time required by the apprentice to do the job Let the completed job = 1 : From the given information, we know the roofer worked 6 hrs, the apprentice 14 hrs : Write a shared work equation + = 1 multiply 10a, results: 6a + 10(14) = 10a 140 = 10a - 6a 140 = 4a a = a = 35 hrs apprentice working alone : : Check this out, + = .6 + .4 = 1
 Miscellaneous_Word_Problems/522110: A man sold half an egg ore than half his eggs. He then sold half an egg more than half his remaining eggs. He did the same a third time, and then he had 7 eggs left. How many eggs he had at first?1 solutions Answer 346840 by ankor@dixie-net.com(15746)   on 2011-10-27 19:06:18 (Show Source): You can put this solution on YOUR website!A man sold half an egg more than half his eggs. e - (.5e+.5) e - .5e - .5 .5e - .5 left : He then sold half an egg more than half his remaining eggs. (.5e-.5) - .5(.5e-.5) - .5 .5e - .5 - .25e + .25 - .5 .25e - .75 left : He did the same a third time, and then he had 7 eggs left. (.25e-.75) - .5(.25e-.75) - .5 = 7 .25e - .75 - .125e + .375 - .5 = 7 .125e - .875 = 7 .125e = 7 + .875 .125e = 7.875 e = e = 63 eggs to start with : : Check this by substituting at each stage of the problem 1st: .5(63) -.5 = 30 eggs 2nd: .25(63) -.75 = 15 eggs last: .125(63)-.875 = 7 eggs
 Numeric_Fractions/522129: What is the fraction of .3654? Please show how you got the answer. Thank you!1 solutions Answer 346823 by ankor@dixie-net.com(15746)   on 2011-10-27 18:39:39 (Show Source): You can put this solution on YOUR website!What is the fraction of .3654? : Just like you say it, 3654 ten-thousandths reduce by dividing numerator and denominator by 2 , is about as reduced as you can get it
 Exponents/522068: could you please help me out i have a maths assignement and i dont know what to do 1. P to the power of two * P to the power of five * P all divided by P to the power of six1 solutions Answer 346782 by ankor@dixie-net.com(15746)   on 2011-10-27 17:16:08 (Show Source): You can put this solution on YOUR website!1. P to the power of two * P to the power of five * P all divided by P to the power of six : Assume the problem is: When you multiply like terms, you add the exponents, (P is assumed to have an exponent of 1) = When you divide like terms you, subtract the exponents =
 Travel_Word_Problems/522219: Hi, this has me stumped: Two drivers 240 miles apart start toward each other at 2pm. The faster one averages 50 mph and the slower one averages 35mph. The faster one stops for 2 hours along the way before they pass each other. Write the equation to determine how long it will take them before they pass each other. I cant sort out how to express the 2 hours of not traveling... this is what I have so far: 240-35t= 50*(4.8-2.0) Above, I'm not sure if I should be subtracting 2 or adding 2 or if that equation is even right :/1 solutions Answer 346763 by ankor@dixie-net.com(15746)   on 2011-10-27 15:43:50 (Show Source): You can put this solution on YOUR website!Two drivers 240 miles apart start toward each other at 2pm. The faster one averages 50 mph and the slower one averages 35mph. The faster one stops for 2 hours along the way before they pass each other. Write the equation to determine how long it will take them before they pass each other. : Let t = travel time of the slower car then (t-2) = travel time of the faster : When they do pass each other the sum of their travel distances = 240 Write a dist equation: dist = speed * time : fast car dist + slow car dist = 240 mi 50(t-2) + 35t = 240
 Quadratic_Equations/522256: To save materials; Choma decides to build a horse corral using the barn for one side. He has 30m of fencing materials and wants the corral to have an area of 100m^2. What are the dimensions of the corral? Let w =width and y = length 2x+y=30 but that's as far as I know how to solve this equation1 solutions Answer 346757 by ankor@dixie-net.com(15746)   on 2011-10-27 15:32:39 (Show Source): You can put this solution on YOUR website!He has 30m of fencing materials and wants the corral to have an area of 100m^2. What are the dimensions of the corral? Let x =width and y = length 2x+y=30 Change to a form we can use for substitution y = (30-2x) : The area x * y = 100 replace y with (30-2x) x(30-2x) = 100 -2x^2 + 30x - 100 = 0; a quadratic equation simplify and change the sign to make it easier to factor, divide by -2 x^2 - 15x + 50 = 0 Factors to (x-10)(x-5) = 0 two solutions x = 5 meters, then y = 20 meters is the length (5*20=100) x = 10 meters, then y = 10 meters is the length (10*10=100) : Check both these solutions to ensure 30 m of fencing is used
 Miscellaneous_Word_Problems/521807: This isn't giving me answers that make sense, what am I missing? The number of board feet (b) of lumber in a 2" by 6" board of length L (in feet) is given by the equation b=8.25/144*L Determine the number of board feet in 2" by 6" boards of length 12ft, 16ft and 20ft I am to come up with 3 answers based on the 3 different lengths and I keep getting decimals. I dont think the answer to 12 feet should be .6874992 1 solutions Answer 346643 by ankor@dixie-net.com(15746)   on 2011-10-26 21:59:39 (Show Source): You can put this solution on YOUR website!It's been a long time since I have used board-feet, but I think where it says "length L (in feet)", is wrong, you have to convert the length into inches. For example, a 12 ft board b = * (12*12) = 8.25 board feet
 Travel_Word_Problems/521822: a train travels on a section at a speed of 48 mph. to the nearest tenth what is the trains speed in feet per min 1 solutions Answer 346633 by ankor@dixie-net.com(15746)   on 2011-10-26 21:43:02 (Show Source): You can put this solution on YOUR website!a train travels on a section at a speed of 48 mph. to the nearest tenth what is the trains speed in feet per min : = 4,224 ft/min
 Human-and-algebraic-language/521700: i need help turning this phrase into a mathematical expression four times a number, subtracted from the sum of the number and three.1 solutions Answer 346629 by ankor@dixie-net.com(15746)   on 2011-10-26 21:27:45 (Show Source): You can put this solution on YOUR website!Just write what it says. n = "the number" : "four times a number, subtracted from the sum of the number and three. n + 3 - 4n
 Numbers_Word_Problems/521530: Three times the ten digit of a certain two-digit number is two more than four times the units digit. The difference between the given number and the number obtained by reversing the digits is two less than twice the sum of the digits. Find the number.1 solutions Answer 346618 by ankor@dixie-net.com(15746)   on 2011-10-26 20:43:23 (Show Source): You can put this solution on YOUR website!let x = the 10's digit Let y = the units then 10x+y = "certain number" : Write an equation for each statement: : "Three times the ten digit of a certain two-digit number is two more than four times the units digit." 3x = 4y + 2 3x - 4y = 2 : " The difference between the given number and the number obtained by reversing the digits is two less than twice the sum of the digits." (10x+y) - (10y+x) = 2(x+y) - 2 10x + y - 10y - x = 2x + 2y -3 9x - 9y = 2x + 2y - 2 9x - 2x - 9y - 2y = -2 7x - 11y = -2 : Use these two simplified equations for elimination Mult the 1st by 7, mult the 2nd by 3 21x - 28y = 14 21x - 33y = -6 ----------------subtraction eliminates x, find y 0 + 5y = 20 y = 20/5 y = 4 : Use 3x = 4y +2, replace y with 4 3x = 4(4) + 2 3x = 18 x = 18/3 x = 6, then 64 is the number : : Check this in the statement: " The difference between the given number and the number obtained by reversing the digits is two less than twice the sum of the digits." 64 - 46 = 2(6+4) - 2 18 = 2(10) - 2
 Numbers_Word_Problems/521532: When a certain three digit number is divided by the number with digits reversed, the quotient is 2 and the remainder is 25. The tens digit is one less than twice the sum of the hundreds digits and units digit. If the units digit is subtracted from the tens digit, the result is twice the hundreds digits. Find the number.1 solutions Answer 346567 by ankor@dixie-net.com(15746)   on 2011-10-26 17:45:01 (Show Source): You can put this solution on YOUR website!let a = the 100's digit let b = the 10's let c = the units then 100a + 10b + c = the number : Write an equation for each statement: : "When a certain three digit number is divided by the number with digits reversed, the quotient is 2 and the remainder is 25." = 2 + multiply thru by 100c+10b+a, results get rid of the denominators: 100a+10b+c = 2(100c+10b+a) + 25 : 100a + 10b + c = 200c + 20b + 2a + 25 Combine like terms 100a - 2a = 200c - c + 20b - 10b + 25 : 98a = 199c + 10b + 25 : : " The tens digit is one less than twice the sum of the hundreds digits and units digit." b = 2(a+c) - 1 b = 2a + 2c - 1 : " If the units digit is subtracted from the tens digit, the result is twice the hundreds digits." b - c = 2a b = c + 2a : b=b, therefore 2a + 2c - 1 = c + 2a Subtract 2a from both sides: 2c - 1 = c 2c - c = 1 c = 1 : The 1st equation simplified 98a = 199c + 10b + 25 replace c with 1, in both equations 98a = 199 + 10b + 25 98a = 10b + 224 : b = 2a + c b = (2a+1) : 98a = 10b + 224 substitute for b 98a = 10(2a+1) + 224 98a = 20a + 10 + 224 98a - 20a = 234 78a = 234 a = 234/78 a = 3 : Find b b = 2a + c b = 2(3) + 1 b = 7 then 371 is the number! : : Check this in the 1st statement: = 2 +
 Polynomials-and-rational-expressions/521378: The width and length of a rectangle are given by two consecutive odd integers. The width of the rectangle is less than it's length. Write an expression for the area of the rectangle. 1 solutions Answer 346557 by ankor@dixie-net.com(15746)   on 2011-10-26 15:52:59 (Show Source): You can put this solution on YOUR website!The width and length of a rectangle are given by two consecutive odd integers. The width of the rectangle is less than it's length. Write an expression for the area of the rectangle. : Let x = the width then (x+2) = the length : The area A = x(x+2) = x^2 + 2x, is the area
 Circles/521597: A square and a circle intersect so that each side of the square contains a chord of the circle equal in length to the radius of the circle. What is the ratio of the area of the square to the area of the circle? Express your answer as a common fractin in terms of Pie.1 solutions Answer 346556 by ankor@dixie-net.com(15746)   on 2011-10-26 15:49:10 (Show Source): You can put this solution on YOUR website!A square and a circle intersect so that each side of the square contains a chord of the circle equal in length to the radius of the circle. What is the ratio of the area of the square to the area of the circle? Express your answer as a common fraction in terms of Pie. : Let r = the side of the square and the radius of the circle : Square area: circle area: , r^2 cancel leaving
 Geometry_Word_Problems/521622: problem: the gasoline tank on a car can be a box with dimensions 1.5 ft x 2.5 ft x 9 inches. How many gallons of gasoline does it hold and what is the weight of the gasoline in a full tank? I am trying to help my daughter with this and I do not know how to figure out formula for weight1 solutions Answer 346555 by ankor@dixie-net.com(15746)   on 2011-10-26 15:42:34 (Show Source): You can put this solution on YOUR website!problem: the gasoline tank on a car can be a box with dimensions 1.5 ft x 2.5 ft x 9 inches. How many gallons of gasoline does it hold and what is the weight of the gasoline in a full tank? : First we find the volume of the tank in cu/ft Convert 9 in: 9/12 = .75 ft V = 1.5 * 2.5 * .75 = 2.8125 cu/ft : Convert cu/ft to gallons: (1 cu/ft = 7.481 gals) 2.8125 * 7.481 = 21.04 gallons : One gallon of gas weighs about 6.1 lbs (lighter than water which weighs about 8.3 lb per gal) 21.04 * 6.1 = 128.346 lbs, a full tank of gas.
 Numbers_Word_Problems/521287: Please help me to solve this problem There a bus leave the interchange. at the bus stop 1/4 passangers alighted and 12 passangers boarded, at the next bus stop 1/2 passangers alighted and 13 passangers boarded. At the final stop there were 25 passangers alighted the bus. How many passangers at the first bus leave the interchange ?1 solutions Answer 346480 by ankor@dixie-net.com(15746)   on 2011-10-26 08:40:17 (Show Source): You can put this solution on YOUR website!There a bus leave the interchange. Let x = original no. of passengers as the interchange : Write an EXPRESSION for each statement: : at the bus stop 1/4 passengers alighted and 12 passengers boarded, x - x + 12 simplifies to x + 12 : at the next bus stop 1/2 passengers alighted and 13 passengers boarded. [x+12] + 13 x + 6 + 13 x + 19 : At the final stop there were 25 passengers alighted the bus. x + 19 - 25 = 0 x -6 = 0 x = 6 3x = 8(6) 3x = 48 x = 48/3 x = 16 passengers first when bus leaves the interchange ?
 Square-cubic-other-roots/521428: please help me find out what the 3 (small 3 like an exponent but on the other side) is doing if it is on the outside of a square rt of 641 solutions Answer 346479 by ankor@dixie-net.com(15746)   on 2011-10-26 08:27:44 (Show Source): You can put this solution on YOUR website!please help me find out what the 3 (small 3 like an exponent but on the other side) is doing if it is on the outside of a square rt of 64 : That means it's not the square root, but the "cube root" or the third root = 4, see that it can be factored to illustrating that the cube root of 64 = 4
 Travel_Word_Problems/520686: Two train starts from two opposite directions towards each other.the velocity of the first train is 100km/h and the velocity of the second train is 50 km /h.Both the train starts at the same time, initially the time is 0 sec. a pigon which is sitting on the first train starts at the same time towards the other trainas soon as it reaches the second train,it flies back to the first train and so on and its velocity is 200km /h .it conyinues to do so ,flying backwards and towards from one train to the other untill the trais meet.how many km will the pigon have flown before the trains meet and it will move how many itteration?1 solutions Answer 346346 by ankor@dixie-net.com(15746)   on 2011-10-25 19:12:08 (Show Source): You can put this solution on YOUR website!You have to know how far the trains were apart, when they started towards each other.
 Travel_Word_Problems/520641: A boy cycles from his house to a friend's house at 20km per hour and home again at 25km per hour. If his round trip takes 9/10 of an hour, how far is it to his friend's house?1 solutions Answer 346274 by ankor@dixie-net.com(15746)   on 2011-10-25 15:09:40 (Show Source): You can put this solution on YOUR website!A boy cycles from his house to a friend's house at 20km per hour and home again at 25km per hour. If his round trip takes 9/10 of an hour, how far is it to his friend's house? : Let d = the one-way distance to friends house ; Write a time equation, time = dist/speed + = .9 Multiply by 100 to clear the denominators, solve for d
 Radicals/520741: I need help with this problem!!! I am stuck and it's a test problem!!! Thank you! When fighting a fire, the velocity v of water being pumped into the air is modeled by the function v= √2hg, where h represents the maximum height of the water and g represents the acceleration due to gravity (32 ft/s2). The Islip Fire Department must purchase a pump that will propel water 90 feet into the air. Will a pump that is advertised to project water with a velocity of 77 feet per second meet the fire departments need? EXPLAIN mathematically and verbally. 1 solutions Answer 346214 by ankor@dixie-net.com(15746)   on 2011-10-25 10:04:39 (Show Source): You can put this solution on YOUR website!When fighting a fire, the velocity v of water being pumped into the air is modeled by the function v= √2hg, where h represents the maximum height of the water and g represents the acceleration due to gravity (32 ft/s2). : The Islip Fire Department must purchase a pump that will propel water 90 feet into the air. Will a pump that is advertised to project water with a velocity of 77 feet per second meet the fire departments need? EXPLAIN mathematically and verbally. : Find the velocity required, replace h with 90 ft, g with 32 ft/s v = 75.86 ~ 76 ft/sec therefore a pump with a 77 ft/sec will just do it : Find the actual height (h) that a pump with 77 ft/s is able accomplish = 77 = 77 square both sides 64h = 77^2 64h = 5929 h = h = 92.6 ft
 expressions/520349: my son is in 5th grade and his home work tonight says... evaluate the exressions when a=3 b=67 c=489 d=9570 The first problem is 1. 7c 2. 4 . c 3. 3a X b ect. I dont even know where to begin on how to do this! 1 solutions Answer 346125 by ankor@dixie-net.com(15746)   on 2011-10-24 22:00:40 (Show Source): You can put this solution on YOUR website!when a=3 b=67 c=489 d=9570 The first problem is : 1. 7c Replace c with 489, them you have 7 * 489 = 3423 : 2. 4 . c Replace c with 489 again 4 * 489 = 1956 : 3. 3a X b Replace a with 3, replace b with 67 3*3*67 = 603
 Travel_Word_Problems/520255: In a river with a steady current, it takes Cal Q. Leytor six minutes to swim a certain distance upstream, but it takes him only three minutes to swim back. How many minutes would it take him to float this same distance downstream? Please help and thanks!1 solutions Answer 346103 by ankor@dixie-net.com(15746)   on 2011-10-24 21:09:40 (Show Source): You can put this solution on YOUR website!In a river with a steady current, it takes Cal Q. Leytor six minutes to swim a certain distance upstream, but it takes him only three minutes to swim back. How many minutes would it take him to float this same distance downstream? : I makes it easier if we assign a distance to this problem, say 90 meters Then we can find the speed of the swimmer (c) in still water, and the speed of the current (c) ; Upstream: 6(s-c) = 90 Downstream: 3(s+c) = 90 : Simplify, divide the 1st equation by 6, and the 2nd equation by 3, results: s - c = 15 s + c = 30 -------------adding eliminates c, find s 2s = 45 s = s = 22.5 m/min swimmer speed in still water Find c 22.5 + c = 30 c = 30 - 22.5 c = 7.5 is the speed of the current, this is your speed if you drift with the current. Find the time to travel 90 meters = 12 min to drift down stream, the same distance that he swam :
 Word_Problems_With_Coins/520253: Mathew went to the store and sked for change for a \$10.00 bill. He got a handful of nickels, dimes, quarters and dollar bills. He got twice as many quarters as dimes.He got one more nickel than dimes. He got two more dollars than quarters.1 solutions Answer 346067 by ankor@dixie-net.com(15746)   on 2011-10-24 19:34:09 (Show Source): You can put this solution on YOUR website!let n = no. of nickels Let d = no. of dimes Let q = no. of quarters let b = no. dollar bills : Write an equation for each statement: : "Mathew went to the store and sked for change for a \$10.00 bill. He got a handful of nickels, dimes, quarters and dollar bills." .05n + .10d + .25q + 1b = 10.00 ; " He got twice as many quarters as dimes. q = 2d : "He got one more nickel than dimes." n = (d+1) : "He got two more dollars than quarters." b = (q+2) We want each variable in terms of d, replace q with 2d b = (2d+2) : .05n + .10d + .25q + 1b = 10.00 replace n, q, b .05(d+1) + .10d + .25(2d) + (2d+2) = 10.00 .05d + .05 + .10d + .50d + 2d + 2 = 10.00 combine like terms 2.65d + 2.05 = 100 2.65d = 10.00 - 2.05 2.65d = 7.95 d = d = 3 dimes ; I'll let you find the no. of the other coins. check the total that it = \$10
 Travel_Word_Problems/520120: A train leaves Union Staion for Central Station, 216 km away, at 9:00 am. One hour later a train leaves Central Station for Union Station. They will meet at noon. If the second train had started at 9:00 am, and the first train at 10:30 am, they would still have met at noon. Find the speed of each train. 1 solutions Answer 346000 by ankor@dixie-net.com(15746)   on 2011-10-24 15:39:39 (Show Source): You can put this solution on YOUR website!A train leaves Union Station for Central Station, 216 km away, at 9:00 am. One hour later a train leaves Central Station for Union Station. They will meet at noon. If the second train had started at 9:00 am, and the first train at 10:30 am, they would still have met at noon. Find the speed of each train. : Let a = Train A's speed Let b = Train B's speed : When they meet, the sum of their distances will equal 216 km Write a distance equation for each Scenario : From the information given for the 1st scenario, travel times: a = 3 hrs when they meet, b = 2 hrs when they meet 3a + 2b = 216 km : From the information given for the 2nd scenario, travel times: a = 1.5 hrs when they meet, b = 3 hrs when they meet 1.5a + 3b = 216 km : Two equations we can solve 3a + 2b = 216 1.5a+3b = 216 multiply the 2nd equation by 2, subtract the 1st equation 3a + 6b = 432 3a + 2b = 216 ---------------subtraction eliminates a, find b 4b = 216 b = 216/4 b = 54 km/h, speed of train B : Find a 3a + 2b = 216 3a + 2(54) = 216 3a = 216 - 108 3a = 108 a = 108/3 a = 36 km/h, speed of train A : : You can check these solutions in both scenario equations.