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# Recent problems solved by 'mananth'

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 Rate-of-work-word-problems/358405: A tank can be filled in 2 hours by 2 pipes together. The larger pipe can fill it in 3 hours less than the smaller. How long will it take each pipe to fill the tank?1 solutions Answer 255783 by mananth(12270)   on 2010-10-19 05:46:44 (Show Source): You can put this solution on YOUR website!both together take 2 hours so they do 1/2 the job in1 hour .. let smaller pipe take x hours so it will do 1/x of the job in 1 hour .. second pipe takes x-3 hours so it does 1/(x-3) of the job in 1 hour ... 1/x + 1/(x-3)=1/2 x-3+x/x(x-3)=1/2 2x-3=1/2* x(x-3) 2(2x-3)=x(x-3) 4x-6=x^2-3x x^2-3x-4x+6=0 x^2-7x+6=0 x^2-6x-x+6=0 x(x-6)-1(x-6)=0 (x-6)(x-1)=0 x=1 OR 6 x = 1 is not valid so x=6 hours taken by the pipe alone second pipe takes 6-3 = 3 hours to fill the tank ... m.ananth@hotmail.ca
 Travel_Word_Problems/358406: A car traveled the first 100 kilometers of a trip at one speed and the last 135 kilometers at an average of 5 kilometers per hour less. If the entire trip took 5 hours, what was the average speed of the car for the first part of the trip?1 solutions Answer 255781 by mananth(12270)   on 2010-10-19 05:36:30 (Show Source): You can put this solution on YOUR website!A car traveled the first 100 kilometers of a trip at one speed and the last 135 kilometers at an average of 5 kilometers per hour less. If the entire trip took 5 hours, what was the average speed of the car for the first part .. first part 100 km -----------x km/h second part 135 km---------- x-5 km/h ... time first part + time second part = 5 hours 100/x + 135/(x-5)= 5 100(x-5)+135x /x(x-5)=5 100(x-5)+135x =x(x-5)*5 100x-500+135x=5x^2-25x 5x^2-260x+500=0 /5 x^2-52x+100=0 x^2-50x-2x+100=0 x(x-50)-2(x-50)=0 (x-50)(x-2)=0 x=2 OR 50 km/h speed = 50 m/h ... m.ananth@hotmail.ca
 Linear_Equations_And_Systems_Word_Problems/358418: one number is 3 more than twice another number. If their sum is 21, find the numbers1 solutions Answer 255780 by mananth(12270)   on 2010-10-19 05:24:22 (Show Source): You can put this solution on YOUR website!let one number be x the other number will be 2x+3 ... x+2x+3=21 3x+3=21 -3 3x=21-3 3x=18 /3 x=18/3 x= 3 .. the other number = 2x+3= 6+3=9 ... m.ananth@hotmail.ca
 Rate-of-work-word-problems/358410: Six people to can perform a task in 8 days. If we add 2 equally able people, how long would it take?1 solutions Answer 255779 by mananth(12270)   on 2010-10-19 05:21:36 (Show Source): You can put this solution on YOUR website!6 people ----------- 8 days 8 people ------------? indirect variation 6/8*8 = 6 days ...
 Miscellaneous_Word_Problems/358409: Johnny has \$100 now and saves \$10 every month. His brother Jimmy has no money currently and is going to save \$15 per month. In how many months will Jimmy have as much money as Johnny?1 solutions Answer 255778 by mananth(12270)   on 2010-10-19 05:19:48 (Show Source): You can put this solution on YOUR website!johnny 100 + 10 /month Jimmy 15 /month let them have same amount after x months ... 100+10x=15x 15x-10x=100 5x=100 x= 20 months ... m.ananth@hotmail.ca .. check 15*20=300 20*10+100=300
 Miscellaneous_Word_Problems/358411: Mary and Jane work part time for a library. Mary works every third day; Jane works every fifth day. Today, they are both working together. In how many days will they be working together again?1 solutions Answer 255777 by mananth(12270)   on 2010-10-19 05:16:12 (Show Source): You can put this solution on YOUR website!mary works third day Jane works 5th day. the leaset common multiple is 3*5 = 15 today they are working together so they will work in the 1+15 = 16th day together ... m.ananth@hotmail.ca
 Numbers_Word_Problems/358416: find 3 consecutive odd integers such find as that thrice the smallest number is 9 more than twice the third1 solutions Answer 255776 by mananth(12270)   on 2010-10-19 05:04:34 (Show Source): You can put this solution on YOUR website!let the integers be x,x+2,x+4 3x=x+2+x+4+9 3x=2x+15 3x-2x=15 x=15 .. the odd integers are 15,17,19 ... m.ananth@hotmail.ca
 Numbers_Word_Problems/358417: find 3 consecutive even numbers such as that sum of the first and the third consecutive even numbers is equal to the second increased by 501 solutions Answer 255775 by mananth(12270)   on 2010-10-19 05:02:08 (Show Source): You can put this solution on YOUR website!find 3 consecutive even numbers such as that sum of the first and the third consecutive even numbers is equal to the second increased by 50 ... let the consequtive even numbers be x,x+2,x+4 x+x+4=x+2+50 2x+4=x+52 2x-x=48 x=48 .. the numbers are 48,50,52 ... m.ananth@hotmail.ca
 Travel_Word_Problems/358385: An airplane flying north at 200 mph passed over a point on the ground at 2:00 PM. Another airplane at the same altitude passed over the point at 2:30 PM, flying east at 400 mph. At what time were the planes 500 miles apart?1 solutions Answer 255773 by mananth(12270)   on 2010-10-19 04:58:36 (Show Source): You can put this solution on YOUR website!An airplane flying north at 200 mph passed over a point on the ground at 2:00 PM. Another airplane at the same altitude passed over the point at 2:30 PM, flying east at 400 mph. At what time were the planes 500 miles apart? .. North plane 200 mph 2.00pm East plane 400 mph 2.30 pm ... in 1/2 hour north plan has traveled 100 miles. when other plane passes the point. ... they are flying at right angles to each other. when the east bound plane travels 2x miles north bound plane has traveled x+100 miles. ( because speed is half & it has 1/2 hour lead) ... (2x)^(x+100)^2= 500^2 4x^2+x^2+200x+10000=250000 5x^2+200x-240000=0 5x^2+1200x-1000x-240000=0 5x(x+240)-1000(x+240)=0 (x+240)(5x-1000)=0 5(x+240)(x-200)=0 x=200 miles 2x=400 miles: speed = 400 mph time = distance/speed 400/400 = 1 hour .... CHECK 400^2+300^2=500^2
 expressions/358394: 3x+[2x-4y(6-4x]+2y-(-3-x+3y)1 solutions Answer 255772 by mananth(12270)   on 2010-10-19 02:28:59 (Show Source): You can put this solution on YOUR website!3x+[2x-4y(6-4x]+2y-(-3-x+3y) 3x+2x-24y+16xy+2y+3+x-3y Add the common terms 6x-25y+16xy-y ... m.ananth@hotmail.ca
 Percentage-and-ratio-word-problems/358395: If two trains are 120 miles apart and are travelling toward each other at constant rate of 30mph and 40mph respectively.How far apart will they be exactly 1 hr before they meet.1 solutions Answer 255771 by mananth(12270)   on 2010-10-19 02:24:37 (Show Source): You can put this solution on YOUR website!If two trains are 120 miles apart and are travelling toward each other at constant rate of 30mph and 40mph respectively.How far apart will they be exactly 1 hr before they meet. .. add up their speeds 40+30 = 70 mph. they approach 70 miles towards each other in 1 hour. they were 120 miles away. 120-70 = 50 miles. they will be 50 miles away. after one hour. ... m.ananth@hotmail.ca
 Rectangles/358387: In a rectangle the lenght is 2cm longer than it's width & a diagonal is 10cm. What is the area?? PLease tell me the answer and how did u get it. ^^ tnx1 solutions Answer 255770 by mananth(12270)   on 2010-10-19 02:21:34 (Show Source): You can put this solution on YOUR website!In a rectangle the lenght is 2cm longer than it's width & a diagonal is 10cm. What is the area?? let the width be x cm length = x+2 cm. .. diagonal = 10 cm. the diagonal and the sides of the rectangle form a right triangle with diagonal as the hypotenuse. use pythagoras theorem . leg1^2+leg2^2= hypo^2 x^2+(x+2)^2= 10^2 x^2+x^2+4x+4 = 100 2x^2+4x+4-100=0 2x^2+4x-96=0 /2 x^2+2x-48=0 x^2+8x-6x-48=0 x(x+8)-6(x+8)=0 (x+8)(x-6)=0 x=6 which is positve width 6 cm length = 8 cm. Area = L*W Area = 6*8=48 cm^2 ... m.ananth@hotmail.ca
 Equations/358356: A leather coin purse has the shape of a triangle. Two sides are equal in length and the third side is 3cm shorter than one and one half times the length of the equal sides. the perimeter is 28.5 cm. find the lengths of the sides.1 solutions Answer 255756 by mananth(12270)   on 2010-10-18 23:42:53 (Show Source): You can put this solution on YOUR website!let the equal sides be x the third side = x/2-3 .. x+x+x/2 -3=28.5 5x/2 = 28.5+3 5x/2=31.5 5x=63 /5 x=63/5 x=12.6 cm the equal sides third side = 6.3 ... m.ananth@hotmail.ca
 Travel_Word_Problems/358377: a boat takes 3 hours to go 24 miles upstream.it can go 36 miles downstream in the same time,Find the speed of the current and the speed of the boat in still water if x=the speed of the boat in still water and y=the speed of the current.1 solutions Answer 255753 by mananth(12270)   on 2010-10-18 23:36:49 (Show Source): You can put this solution on YOUR website!a boat takes 3 hours to go 24 miles upstream.it can go 36 miles downstream in the same time,Find the speed of the current and the speed of the boat in still water if x=the speed of the boat in still water y=the speed of the current. downstream speed = x+y upstream speed = x-y ... time downstream = 36/(x+y)=3 3x+3y=36 time upstream = 24/(x-y)=3 3x-3y=24 add the equations 6x=60 /6 x= 10 mph speed of boat ... plug value of x in equation 30+3y=36 3y=36-30 3y=6 y=2 mph speed of current ... m.ananth@hotmail.ca
 Functions/358374: write the equation as a function of s: 5=t+6s1 solutions Answer 255752 by mananth(12270)   on 2010-10-18 23:30:22 (Show Source): You can put this solution on YOUR website!5=t+6s add -t to both sides 5-t=t-t+6s 5-t=6s divide by 6 5/6 -t/6 = y .. y=-t/6 +5/6 ... m.ananth@hotmail.ca
 test/358354: Solve the equation for y: 2x+3y=91 solutions Answer 255751 by mananth(12270)   on 2010-10-18 23:28:20 (Show Source): You can put this solution on YOUR website!2x+3y=9 add -2x -2x+2x+3y=9-2x 3y=9-2x divide by 3 3y/3 = 9/3-2x/3 y = 3-2x/3 ... m.ananth@hotmail.ca
 test/358357: -6x-4<381 solutions Answer 255749 by mananth(12270)   on 2010-10-18 23:25:36 (Show Source): You can put this solution on YOUR website!-6x-4<38 add 4 -6x+4-4<38+4 -6x<42 divide by -6 x>7 ... m.ananth@hotmail.ca
 Money_Word_Problems/358362: debra invested \$18000.Part of it was invested at 3% annual simple interest, and the rest was invested at 4%. Her interest income for the first year was \$650.How much did she invest at each rate?1 solutions Answer 255747 by mananth(12270)   on 2010-10-18 23:22:45 (Show Source): You can put this solution on YOUR website!debra invested \$18000.Part of it was invested at 3% annual simple interest, and the rest was invested at 4%. Her interest income for the first year was \$650.How much did she invest at each rate? ... \$x @ 3% 18000-x@4% Interest = 650 ... 3x+4(18000-x)=65000 3x+72000-4x=65000 -x=-7000 x= \$7000 @ 3% balance \$11000 @4% ... m.ananth@hotmail.ca
 Linear-equations/358364: Find the equation( in slope intercept form)of the line passing through the points given coordinates(-4,0) ,(-1,2)1 solutions Answer 255743 by mananth(12270)   on 2010-10-18 23:17:09 (Show Source): You can put this solution on YOUR website!slope = y2-y1/x2-x1 =2-0/-1-(-4) =2/3 ... y=mx+b Take any point (-4,0) plug x,y,m to get b 0=2/3*-4 +b 0=-8/3 b= 8/3 ... equation = y=(2x/3)+8/3 ... m.ananth@hotmail.ca
 Geometry_Word_Problems/358367: a building casts a shadow 40 ft long when the sun's angle of elevation is 58 degrees. Find the height of the building.1 solutions Answer 255741 by mananth(12270)   on 2010-10-18 23:07:12 (Show Source): You can put this solution on YOUR website!a building casts a shadow 40 ft long when the sun's angle of elevation is 58 degrees. Find the height of the building. ... let the height of building be x tan(58 degrees) = x/40 1.60033453 = x/40 x = 1.60033453 * 40 x = 64.01 feet ... m.ananth@hotmail.ca