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# Recent problems solved by 'Paul'

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 Human-and-algebraic-language/61430: joseph and caleb drove together for seven hours. So far, they have driven three hundred twenty- five miles. Joseph drove the first three hours. Caleb drove the rest of the way at a speed twenty- six less than two times Joseph's speed (in miles per hour). What was Caleb's average driving speed?1 solutions Answer 42320 by Paul(988)   on 2006-11-15 00:31:44 (Show Source): You can put this solution on YOUR website!Jeseph drove for 3 hours and celeb drove for 4 hours EQUATION: 3(x)+4(2x-26)=325 3x+8x-104=325 11x=429 x=39 2(39)-26=52 Hence, Jeseph drove at 39mph and Caleb drove at 52mph. Paul.
 Miscellaneous_Word_Problems/58814: This question is from textbook college algebra please help me set up and solve. Thank You! During summer vacation, Hector and Ann earned a total of \$1088. Hector worked 8 days fewer than Ann and earned \$2 per day less. Find the number of days he worked and the daily wage he made if the total number of days worked by both was 72.1 solutions Answer 40340 by Paul(988)   on 2006-10-29 19:59:09 (Show Source): You can put this solution on YOUR website!Let x repsent the amount of days Ann worked Hector worked for x-8 days NUMBER OF DAYS: x+x-8=72 2x=80 x=40 40-8=32 Hector worked for 32 days and Ann worked for 40 days EQAUTION: 32(x-2)+40x=1088 72x=1152 x=16 32(16-2)=448 40(16)=640 Hence, HEctor worked for 32 days and had a payment of \$448 Paul.
 Travel_Word_Problems/58613: This question is from textbook Elementary Algebra Hope someone can help quick - I have a test on Monday and am having terrible difficulty with the story probs. Here's one problem: "Plane took 1 hr. LONGER to fly 480 AGAINST the wind than it took to fly the same distance WITH the wind. If wind speed is 20 mph, what is the speed of plane in calm air?" I don't know how to figure speed of plane just based on air speed. All I know is distance is 480 both ways and time taken is "x + 1" for against wind and "x" for with wind. Can you help? 1 solutions Answer 40153 by Paul(988)   on 2006-10-28 13:35:11 (Show Source): You can put this solution on YOUR website!EQUATION: 480((x+20)-(x-20))=(x-20)(x+20) x=140 Hence, the speed of the plane is 140mph. Paul.
 Travel_Word_Problems/57404: This question is from textbook Algebra: Structure and Method Jan can run at 7.5 m/s and Mary at 8.0 m/s. On a race track Jan is given a 25 m head start, and the race ends in a tie. How long is the track?1 solutions Answer 39156 by Paul(988)   on 2006-10-21 18:49:06 (Show Source): You can put this solution on YOUR website!Let x represent the length of the track EQUATION: 7.5x+25=8x 0.5x=25 x=50 Hence, the track is 50m long. Paul.
 Miscellaneous_Word_Problems/55630: Two isosceles triangles have the same base length. The legs of one of the triangles are twice as long as the legs of the other. Find the lengths of the sides of the triangles if their perimeters are 23 cm and 41 cm.1 solutions Answer 37745 by Paul(988)   on 2006-10-10 23:44:26 (Show Source): You can put this solution on YOUR website!Let y represent the base Let x represent the side length EQUATION: x+x+y=23 2x+y=23 y=23-2x EQUATION 2: 2x+2x+y=41 SUBSITUTE FOR Y: 4x+(23-2x)=41 2x=18 x=9 y=23-2(9) y=5 Hence, the length of the sides are 9 and 2(9)=18cm Paul.
 Travel_Word_Problems/55601: Joan ran from her home to the lake at 8 mi/h. She ran back home at 6 mi/h. Her total running time was 1 hour. How much time did it take Joan to run from her home to the lake?1 solutions Answer 37738 by Paul(988)   on 2006-10-10 22:37:53 (Show Source): You can put this solution on YOUR website!Let x represent the time: 8x=6(1-x) 8x=6-6x 14x=6 x=3/7 Hence, it took her 3/7 hours Paul.
 Linear_Equations_And_Systems_Word_Problems/55240: Four men were shipwrecked on an island. The first day they gathered a pile of coconuts and then went to sleep. During the night one of the men woke up and ate 1/3 of the coconuts. A second man woke up and ate 1/3 of the remaining cocnuts. A third man did the same. When the fourth man woke up he ate 1/4 of the remaining cocnuts. Then there were 6 coconuts left. How many coconuts did the men gather?1 solutions Answer 37513 by Paul(988)   on 2006-10-09 12:25:49 (Show Source): You can put this solution on YOUR website! EQUATION 36x-12x-4(2x)-4x=6(108) 12x=108 x=54 Hence, there were 54 coconuts Paul.
 Linear-equations/54889: Gina has \$2 more than three times the amount that Fred has. When Gina gabe Fred \$5, Fred then had one-half as much as Gina. How much did Gina have at first? Write an equation.1 solutions Answer 37104 by Paul(988)   on 2006-10-06 00:18:40 (Show Source): You can put this solution on YOUR website!Fred has \$x Gina has \$2+3x EQUATION: x=13 2(13)+2=41 Hence, Gina had \$41 at first Paul.
 Travel_Word_Problems/53741: one car travels 50 miles per hour and another one travels 55 miles per hour. if they start from the same place at the same time and travel in the same direction, after how many hours will the faster car be 35 miles ahead of the slower car?1 solutions Answer 35991 by Paul(988)   on 2006-09-26 23:43:04 (Show Source): You can put this solution on YOUR website!let x represent the time 50x+35=55x 5x=35 x=7 Hence, in 7 hours. Paul.
 Numbers_Word_Problems/53725: A man is 2/5 the way walking accross a railroad bridge whenhe hears a train approaching from behind him. He can reach either end of the bridge just as the train reaches the same point. If the trainis traveling at 60 miles per hour(mph), at what average speed must the man run?1 solutions Answer 35945 by Paul(988)   on 2006-09-26 20:18:47 (Show Source): You can put this solution on YOUR website!2(2/5)=4/5 5/5-4/5=1/5 That means that the man would run 1/5 of the bridge, and it would take the train to run the whole 5/5 of the bridge 1x/5=5/5 x=5 60/5=12 Hence, the speed of the man is 12mph. Paul.
 Angles/53180: Three times the complement of an angle less the supplement of an angle is 10 degrees. Find the supplement.1 solutions Answer 35461 by Paul(988)   on 2006-09-21 21:39:40 (Show Source): You can put this solution on YOUR website!(180-x)-3(90-x)=10 -90+2x=10 2x=100 x=50 Hence, the angle is 50 degrees Paul.
 Rate-of-work-word-problems/53079: A 5-horsepower (hp) pump can empty a pool in 5 hours. A smaller, 2-hp pump empties the same pool in 8 hours. The pumps are used together to start emptying the pool. After three hours, the 2-hp pump breaks down. How much longer will it take the larger pump to finish emptying the pool, in hours and minutes?1 solutions Answer 35387 by Paul(988)   on 2006-09-20 23:37:08 (Show Source): You can put this solution on YOUR website!Together: 3 HOurs: --> so there is left: EQUATION: Solve and u get x=0.125 or 0.125(60)=7.5 minutes. Paul.
 Geometry_Word_Problems/52663: Find the measure of an angle whose supplement is 45 degrees more then twice its complement.1 solutions Answer 35130 by Paul(988)   on 2006-09-17 23:36:05 (Show Source): You can put this solution on YOUR website!supplement = 180-x Complement = 90-x EQUATION: 180-x=45+2(90-x) solve from there Paul.
 Travel_Word_Problems/52662: Here is my problem: Bob roller blades 9 miles each morning. Today, he averaged 10 mph for the first 6 miles and 5 mph for the remaining 3 miles. How long did the entire trip take? I came up with the solution of 1 hour and 12 minutes, with 10 mph for six miles taking 36 minutes and 5 mph for 3 miles taking also 36 minutes. My problem is I don't know how to show the steps of how I came to that answer. I know that the... Distance = 9 miles Rate = 10 mph for 6 miles & 5 mph for 3 miles Time = unknown variable ...I just don't know the best way to show my answer to the problem? Could you help me please? Thank you so much in advance! Kellye1 solutions Answer 35129 by Paul(988)   on 2006-09-17 23:34:25 (Show Source): You can put this solution on YOUR website!First set up the equation: Speed=distance/time so time =distance/speed Let x represent the time: so: 6+6=10x x=1.2 Hence, the total time was 1.2hours. Paul.
 Travel_Word_Problems/52497: A boy travels to school going 3 mph and on the way home, it is the same distance, but he goes at 5 mph instead. The entire roundtrip took one hour... what was the distance (in miles) that he traveled? 1 solutions Answer 35066 by Paul(988)   on 2006-09-17 00:49:01 (Show Source): You can put this solution on YOUR website!Let x represent the distance EQUATION: solve from there. Paul.
 Age_Word_Problems/52394: The ages of Ann and Bill add up to 91. Ann is now three times as old as bill was at the time when Ann was twice as old as Bill is now. How old are Ann and Bill now? Please give an explanation or place where I can find this information. Thanks.1 solutions Answer 34968 by Paul(988)   on 2006-09-15 23:44:32 (Show Source): You can put this solution on YOUR website!Ann is 3(2x) years old Bill is x years old EQUATION: 3(2x)+x=91 7x=91 x=13 91-13=78 Hence, Bill is 13 and Ann is 78 Paul.
 Rate-of-work-word-problems/52417: How do you solve this working together problem? Patrice, by himself, can paint four rooms in 10 hours. If he hires April to help, they can do the same job together in 6 hours. If he lets April work alone, how long will it take her to paint four rooms?1 solutions Answer 34966 by Paul(988)   on 2006-09-15 23:31:10 (Show Source): You can put this solution on YOUR website!April can do the job is x hours; EQUATION: 10x-6x=60 4x=60 x=15 Hence, April can do the job in 15 hours. Paul.
 Travel_Word_Problems/52114: When Sheila asked Margie to deliver camp supplies across the lake, they agreed to meet on the water. Sheila's boat can travel at 10km/h, while Margies boat can do 12km/h. If the lake is 6.6 km wide and Sheila and Margie leave at the same time, how much time will it be before they meet?1 solutions Answer 34773 by Paul(988)   on 2006-09-13 20:42:53 (Show Source): You can put this solution on YOUR website!10x+12x=6.6 22x=6.6 x=0.3 Hence they will meet in 18 minutes. Paul.
 Angles/51574: the measue of the supplement of an angle is 60 less than three times the measure of the complement of the angle. Find the measure of the angle.1 solutions Answer 34398 by Paul(988)   on 2006-09-10 13:31:41 (Show Source): You can put this solution on YOUR website!Let x be the angle EQUATION: 180-x=3(90-x)-60 SOlve froom there. Paul.
 Equations/51453: The triangles in each pair are similar. Find the unknown side length. click for link: http://img1.imagetitan.com/img1/1/27/math.jpg Question submitted by: Sumeet M1 solutions Answer 34392 by Paul(988)   on 2006-09-10 12:55:15 (Show Source): You can put this solution on YOUR website!To find x: EQUATION: 3x=6*4 3x=24 x=8 PAUL>
 Miscellaneous_Word_Problems/51443: During the first 4 hours of a trip, you average 40MPH. How long must you travel at 60MPH to finish with an overall average speed of 55MPH?1 solutions Answer 34391 by Paul(988)   on 2006-09-10 12:37:31 (Show Source): You can put this solution on YOUR website!let x be the time EQUATION: 40(4)+60x=55(x+4) 160+60x=55x+220 5x=60 x=12 HEnce, you must travel for 12 hours. Paul.
 Human-and-algebraic-language/50857: Martina went shopping. She spent one-fifth of what she had in her wallet and then one-fifth of what remained. In all she spent \$36. How much did she start with? Can you help me with this problem? Thank you!1 solutions Answer 33910 by Paul(988)   on 2006-09-05 20:30:19 (Show Source): You can put this solution on YOUR website!let x be the amount of money in her wallet EQUATION: x=900 hence, she started off with \$900 Paul.
 Travel_Word_Problems/50777: A motorist drove 150 miles on country roads before driving on mountain roads. The rate of speed on the country roads was three times the rate on the mountain roads. The total time spent traveling the 200 miles was five hours. Find the rate of the motorist on the country roads.1 solutions Answer 33814 by Paul(988)   on 2006-09-04 20:32:25 (Show Source): You can put this solution on YOUR website!Let the speed on the country road be 3x x = mountain speed 50 miles were driven on mountain road EQUATION: x=0 or x=20 20(3)=60 Hence, the speed on the country road was 60mph. Paul.
 Miscellaneous_Word_Problems/50575: The measure of a supplement of an angle is 12 degrees greater than three times the measure of a complement. Find the measure of the angle.1 solutions Answer 33641 by Paul(988)   on 2006-09-02 18:11:10 (Show Source): You can put this solution on YOUR website!supplement = 180-x complement = 90-x EQUATION: 180-x=12+3(90-x) 180-x=12+270-3x 2x=102 x=51 Hence, the measure of the angle is 51 degrees Paul.
 Rectangles/50198: This question is from textbook Geometry Find the minimum perimeter of a rectangle whose area is 169 square meters. I know the answer is 52 meters, but I don't know how they got the answer. 1 solutions Answer 33412 by Paul(988)   on 2006-08-30 20:16:03 (Show Source): You can put this solution on YOUR website!xy=169 x=length y=width y=169/x Perimeter:2x+2y=P x=13 y=13 so 2(13)+2(13)=52 Paul.
 Age_Word_Problems/50170: Eight years ago, Mary was half as old as Jane will be when jane is one year older than Tim will be at the time when Mary will be five times as old as Tim will be two years from now.1 solutions Answer 33384 by Paul(988)   on 2006-08-30 16:45:30 (Show Source): You can put this solution on YOUR website!I think ur question is not complete. PLease type a compelete question.
 Expressions-with-variables/50052: Kyle had 36 books in his locker. Some were library books, some were textbooks, and the rest were telephone books. The number of library books and telephone books combined equals twice the number of textbooks. The number of textbooks and telephone books combined equals three times the number of library books. How many of each type of book were in Kyle's locker?1 solutions Answer 33313 by Paul(988)   on 2006-08-29 13:15:13 (Show Source): You can put this solution on YOUR website!Let x be the libaray books, y be the textbooks and z be the telephone books EQUATION 1: x+y+z=36 EQUATION 2: x+z=2y ---> EQUATION 3: y+z=3x SUb EQUATION 2 into 1 and 3 3x+3z=72 (EQUATION 4) 3z-5x=0 (EQUATION 5) Subtract equation4 from 5 and simplfy: 3x-(-5x)=72 3x+5x=72 8x=72 x=9 3z=5x 3z=5(9) z=15 y=(x+z)/2 y=12 so hence, there are 9 libaray books, 12 textbooks and 15 telephone books in the locker. Paul.
 Travel_Word_Problems/50067: The problem is: Michael drove to a friend's house at a rate of 40mi/h. He returned by the same route at a rate of 45mi/h. the driving time for the round trip was 4 h. What was the distance Michael traveled? I know the answer is about 170 miles because (45+40)/2 is 42.5 times 4 is 170. But how do you set up an algebraic equation to solve?1 solutions Answer 33309 by Paul(988)   on 2006-08-29 12:51:27 (Show Source): You can put this solution on YOUR website!Let x be the distance because time = distance/speed 45*40=1800 40x+45x=7200 85x=7200 x=84.7 the answer is not 170 Paul.
 Numbers_Word_Problems/50017: the tens digit t of a two digit number is 2 less than the ones digit u. if the digits are reversed, the result is 5 more than twice the original number. what was the original number?1 solutions Answer 33251 by Paul(988)   on 2006-08-28 16:23:18 (Show Source): You can put this solution on YOUR website!ten digit y = x-2 one digit = x Original number = 10y+x Reversed number = 10x+y EQUATION: 10x+y=5+2(10y+x) SUBSITUTE FOR Y: 10x+(x-2)=5+20y+2x 11x-2=5+20(x-2)+2x 11x-2=22x-35 11x=33 x=3 y=3-2=1 Hence, the number is 13. Paul.
 Miscellaneous_Word_Problems/50020: the sum of two numbers is 13. if the second number is divided by the first, the quotient will be 2 with a remainder of 1. what are the numbers?1 solutions Answer 33250 by Paul(988)   on 2006-08-28 16:18:44 (Show Source): You can put this solution on YOUR website!Let x and y be the numbers x+y=13 y=13-x simplfy and solve x=4 y=13-4=9 Hence, thr two numbers are 4 and 9. Paul.