Algebra ->  Tutoring on algebra.com -> See tutors' answers!      Log On

 Tutoring Home For Students Tools for Tutors Our Tutors Register Recently Solved
 By Tutor
| By Problem Number |

Tutor:

# Recent problems solved by 'mananth'

Jump to solutions: 0..29 , 30..59 , 60..89 , 90..119 , 120..149 , 150..179 , 180..209 , 210..239 , 240..269 , 270..299 , 300..329 , 330..359 , 360..389 , 390..419 , 420..449 , 450..479 , 480..509 , 510..539 , 540..569 , 570..599 , 600..629 , 630..659 , 660..689 , 690..719 , 720..749 , 750..779 , 780..809 , 810..839 , 840..869 , 870..899 , 900..929 , 930..959 , 960..989 , 990..1019 , 1020..1049 , 1050..1079 , 1080..1109 , 1110..1139 , 1140..1169 , 1170..1199 , 1200..1229 , 1230..1259 , 1260..1289 , 1290..1319 , 1320..1349 , 1350..1379 , 1380..1409 , 1410..1439 , 1440..1469 , 1470..1499 , 1500..1529 , 1530..1559 , 1560..1589 , 1590..1619 , 1620..1649 , 1650..1679 , 1680..1709 , 1710..1739 , 1740..1769 , 1770..1799 , 1800..1829 , 1830..1859 , 1860..1889 , 1890..1919 , 1920..1949 , 1950..1979 , 1980..2009 , 2010..2039 , 2040..2069 , 2070..2099 , 2100..2129 , 2130..2159 , 2160..2189 , 2190..2219 , 2220..2249 , 2250..2279 , 2280..2309 , 2310..2339 , 2340..2369 , 2370..2399 , 2400..2429 , 2430..2459 , 2460..2489 , 2490..2519 , 2520..2549 , 2550..2579 , 2580..2609 , 2610..2639 , 2640..2669 , 2670..2699 , 2700..2729 , 2730..2759 , 2760..2789 , 2790..2819 , 2820..2849 , 2850..2879 , 2880..2909 , 2910..2939 , 2940..2969 , 2970..2999 , 3000..3029 , 3030..3059 , 3060..3089 , 3090..3119 , 3120..3149 , 3150..3179 , 3180..3209 , 3210..3239 , 3240..3269 , 3270..3299 , 3300..3329 , 3330..3359 , 3360..3389 , 3390..3419 , 3420..3449 , 3450..3479 , 3480..3509 , 3510..3539 , 3540..3569 , 3570..3599 , 3600..3629 , 3630..3659 , 3660..3689 , 3690..3719 , 3720..3749 , 3750..3779 , 3780..3809 , 3810..3839 , 3840..3869 , 3870..3899 , 3900..3929 , 3930..3959 , 3960..3989 , 3990..4019 , 4020..4049 , 4050..4079 , 4080..4109 , 4110..4139 , 4140..4169 , 4170..4199 , 4200..4229 , 4230..4259 , 4260..4289 , 4290..4319 , 4320..4349 , 4350..4379 , 4380..4409 , 4410..4439 , 4440..4469 , 4470..4499 , 4500..4529 , 4530..4559 , 4560..4589 , 4590..4619 , 4620..4649 , 4650..4679 , 4680..4709 , 4710..4739 , 4740..4769 , 4770..4799 , 4800..4829 , 4830..4859 , 4860..4889 , 4890..4919 , 4920..4949 , 4950..4979 , 4980..5009 , 5010..5039 , 5040..5069 , 5070..5099 , 5100..5129 , 5130..5159 , 5160..5189 , 5190..5219 , 5220..5249 , 5250..5279 , 5280..5309 , 5310..5339 , 5340..5369 , 5370..5399 , 5400..5429 , 5430..5459 , 5460..5489 , 5490..5519 , 5520..5549 , 5550..5579 , 5580..5609 , 5610..5639 , 5640..5669 , 5670..5699 , 5700..5729 , 5730..5759 , 5760..5789 , 5790..5819 , 5820..5849 , 5850..5879 , 5880..5909 , 5910..5939 , 5940..5969 , 5970..5999 , 6000..6029 , 6030..6059 , 6060..6089 , 6090..6119 , 6120..6149 , 6150..6179 , 6180..6209 , 6210..6239 , 6240..6269 , 6270..6299 , 6300..6329 , 6330..6359 , 6360..6389 , 6390..6419 , 6420..6449 , 6450..6479 , 6480..6509 , 6510..6539 , 6540..6569 , 6570..6599 , 6600..6629 , 6630..6659 , 6660..6689 , 6690..6719 , 6720..6749 , 6750..6779 , 6780..6809 , 6810..6839 , 6840..6869 , 6870..6899 , 6900..6929 , 6930..6959 , 6960..6989 , 6990..7019 , 7020..7049 , 7050..7079 , 7080..7109 , 7110..7139 , 7140..7169 , 7170..7199 , 7200..7229 , 7230..7259 , 7260..7289 , 7290..7319 , 7320..7349 , 7350..7379 , 7380..7409 , 7410..7439 , 7440..7469 , 7470..7499 , 7500..7529 , 7530..7559 , 7560..7589 , 7590..7619 , 7620..7649 , 7650..7679 , 7680..7709 , 7710..7739 , 7740..7769 , 7770..7799 , 7800..7829 , 7830..7859 , 7860..7889 , 7890..7919 , 7920..7949 , 7950..7979 , 7980..8009 , 8010..8039 , 8040..8069 , 8070..8099 , 8100..8129 , 8130..8159 , 8160..8189 , 8190..8219 , 8220..8249 , 8250..8279 , 8280..8309 , 8310..8339 , 8340..8369 , 8370..8399 , 8400..8429 , 8430..8459 , 8460..8489 , 8490..8519 , 8520..8549 , 8550..8579 , 8580..8609 , 8610..8639 , 8640..8669 , 8670..8699 , 8700..8729 , 8730..8759 , 8760..8789 , 8790..8819 , 8820..8849 , 8850..8879 , 8880..8909 , 8910..8939 , 8940..8969 , 8970..8999 , 9000..9029 , 9030..9059 , 9060..9089 , 9090..9119 , 9120..9149 , 9150..9179 , 9180..9209 , 9210..9239 , 9240..9269 , 9270..9299 , 9300..9329 , 9330..9359 , 9360..9389 , 9390..9419 , 9420..9449 , 9450..9479 , 9480..9509 , 9510..9539 , 9540..9569 , 9570..9599 , 9600..9629 , 9630..9659 , 9660..9689 , 9690..9719 , 9720..9749 , 9750..9779 , 9780..9809 , 9810..9839 , 9840..9869 , 9870..9899 , 9900..9929 , 9930..9959 , 9960..9989 , 9990..10019 , 10020..10049 , 10050..10079 , 10080..10109 , 10110..10139 , 10140..10169 , 10170..10199 , 10200..10229 , 10230..10259 , 10260..10289 , 10290..10319 , 10320..10349 , 10350..10379 , 10380..10409 , 10410..10439 , 10440..10469 , 10470..10499 , 10500..10529 , 10530..10559 , 10560..10589 , 10590..10619 , 10620..10649 , 10650..10679 , 10680..10709 , 10710..10739 , 10740..10769 , 10770..10799 , 10800..10829 , 10830..10859 , 10860..10889 , 10890..10919 , 10920..10949 , 10950..10979 , 10980..11009 , 11010..11039 , 11040..11069 , 11070..11099 , 11100..11129 , 11130..11159 , 11160..11189 , 11190..11219 , 11220..11249 , 11250..11279 , 11280..11309 , 11310..11339 , 11340..11369 , 11370..11399 , 11400..11429 , 11430..11459 , 11460..11489 , 11490..11519 , 11520..11549 , 11550..11579 , 11580..11609 , 11610..11639 , 11640..11669 , 11670..11699 , 11700..11729 , 11730..11759 , 11760..11789 , 11790..11819 , 11820..11849 , 11850..11879 , 11880..11909 , 11910..11939 , 11940..11969 , 11970..11999 , 12000..12029 , 12030..12059 , 12060..12089 , 12090..12119 , 12120..12149 , 12150..12179 , 12180..12209 , 12210..12239 , 12240..12269 , 12270..12299, >>Next

 Linear_Equations_And_Systems_Word_Problems/428486: mr. sharma ivested a total of 30,000 in two ventures for a year. the annual return from one of them is 8% and the other paid 10.5% for the year. he recieved a total income of 2250 from both. how much did he invest at each rate??? i need help solving this problem.1 solutions Answer 297829 by mananth(12270)   on 2011-03-29 02:30:26 (Show Source): You can put this solution on YOUR website!Below an interest of Rs 2400 one investment becomes negative. not possible I have worked with Rs. 2550. as interest. instead of Rs 2250. Part I 8.00% per annum Part II 10.50% per annum x + y 30000 ------------------------1 8.00%x+10.50%y= Rs2,550.00 Multiply by 100 8x+10.5y =Rs255,000.00 --------2 Multiply (1) by -8 we get -8x-8y= -240000.00 Add this to (2) 2.5y=\$15,000.00 divide by 2.5 y=Rs.6,000.00 investment at at 10.5% Balance Rs.24,000.00 investment at 8%
 Travel_Word_Problems/428493: Two cars leave towns 750 kilometers apart at the same time and travel toward each other. One car's rate is 10 kilometers per hour less than the other's. If they meet in 5 hours, what is the rate of the slower car? I have no idea how to even start this problem. Is there an equation or what do I do to solve this?1 solutions Answer 297828 by mananth(12270)   on 2011-03-29 02:09:52 (Show Source): You can put this solution on YOUR website!Car A x mph Car B x+ 10 .. They are going away from each other. So add up their speed. combined speed = x+ 1 x + 10 ( 2 x + 10 ) Time = 5 hours Distance = 750 miles Distance = speed * time ( 2 x 10 )* 5 = 750 10 x + 50 = 750 10 x = 750 + -50 10 x = 700 / 10 x= 70 mph Car A Car B 70 + 10 = 80 mph
 Linear_Equations_And_Systems_Word_Problems/428523: One pump can empty a pool in 5 days, whereas a second pump can empty the pool in 7 days. How long will it take the two pumps, working together, to empty the pool? 1 solutions Answer 297827 by mananth(12270)   on 2011-03-29 01:55:36 (Show Source): You can put this solution on YOUR website!Emptying the tank is one job one pipe drains in 5 days It does 1/ 5 of the job in 1 day other pipe 7 day It does 1/ 7 of thejob in 1 day Together they will do 1/5+ 1/ 7 Together they will do 12/35 of the job in one day So they will take 2 8/9 days So they will take 2.92 days
 Mixture_Word_Problems/428518: How many liters of distilled water must be added to 140 liters of an 80% alcohol solution to obtain a 70% solution? i think the answer is 2.3 liters.1 solutions Answer 297826 by mananth(12270)   on 2011-03-29 01:50:04 (Show Source): You can put this solution on YOUR website!------ Percent ---------------- quantity Alcohol 80 ---------------- 140 water 0 ---------------- x Total 70 ---------------- 140+x 80*140+ 0*x=70(140+x) 11200=9800+70x -70x=9800-11200 -70x=-1400 /-70x x=20 gallons water
 Miscellaneous_Word_Problems/428525: An airplane can travewl 380 miles into the wind in the same time that it can travel 420 miles with the wind. If the wind speed is 10 miles per hour, find the speed of the airplane without any wind.1 solutions Answer 297825 by mananth(12270)   on 2011-03-29 01:41:55 (Show Source): You can put this solution on YOUR website!plane speed x mph wind speed 10 mph .. against wind x-10mph with wind x+10 mph Distance against wind 380 Distance with tail wind 420 Time = same 380/(x- 10)= 420/(x+ 10) 380*(x+ 10)= 420*(x- 10) 380x +3800 =420x-4200 420x -380x =4200+3800 40x =8000 /40 x= 200 mph
 Linear_Equations_And_Systems_Word_Problems/428528: Two cars leave town at the same time and travel in the same direction. One car travels one and one-half times as fast as the other car. After 4 hours and 45 minutes, they are 95 miles apart. What is the speed of each car? I don't want you to solve it, I am looking for the two equations for me to solve the linear system. 1 solutions Answer 297824 by mananth(12270)   on 2011-03-29 01:31:53 (Show Source): You can put this solution on YOUR website!Car A x mph Car B 1.5 x mph .. same direction subtract the speed resultant speed = 1.5x-x= 0.5x time = 4 3/4 hour = 4.75 distance = 95 miles d/speed = time 95/0.5x= 4.75 95 = 2.375x x=95/2.375 40 mph Car A Car B = 60 mph
 Linear_Equations_And_Systems_Word_Problems/428527: I just need help setting this up, I can solve it after that. At a Conseesion stand, five hotdog(s) and two hamburger(s) cost \$9.75; two hotdog(s) and five hamburger(s) cost \$11.25, Find the cost of one hotdog and one hamburger.1 solutions Answer 297823 by mananth(12270)   on 2011-03-29 01:24:53 (Show Source): You can put this solution on YOUR website!5x+2y=9.75 .............1 2x+5y=11.25 .............2 multiply (1)by -5 Multiply (2) by 2 -25x-10y =-48.75 4x+10y=22.5 Add the two equations -21x=-26.25 /-21 x=1.25 hotdog cost plug value of x in (1) 5x+2y=9.75 6.25+2y= 9.75 2y=9.75 -6.25 2y=3.5 y=1.75 hamburger cost
 Mixture_Word_Problems/428511: How much pure acid should be mixed with 6 gallons if a 60% acid in order to get a 70% acid solution1 solutions Answer 297818 by mananth(12270)   on 2011-03-28 23:37:02 (Show Source): You can put this solution on YOUR website!.......... Percent ---------------- quantity Solution ..........60----------------30 Pure acid.........100----------------x Total 70 ---------------- 30+x 60*6+100 *x=70(6+ x) 360+100x =420+70x 100x-70 x=420-360 30x=60 /30 x=2 gallons 100 % Pure acid
 Money_Word_Problems/428429: Carl invested \$10,000, part in a CD paying 8.5% annual interest, the rest in a mutual fund paying 7% annual interest. The annual income from the CD is \$200 more than the annual income from the mutual fund. How much money was put into each type of investment?1 solutions Answer 297802 by mananth(12270)   on 2011-03-28 21:44:49 (Show Source): You can put this solution on YOUR website!Part I 8.50% per annum Part II 7.00% per annum x+y=10000 ------------------------1 8.50%x-7.00%y=\$200.00 Multiply by 100 8.5x-7y =\$20,000.00--------2 Multiply (1) by -8.5 we get -8.5x-8.5y=-85000.00 Add this to (2) x-15.5y =-\$65,000.00 divide by -15.5 y=\$4,193.55 investment at7.00% Balance \$5,806.45 investment at 8.50%
 Linear-systems/428381: 5x + 4y = 40 x + 2y = 11 1 solutions Answer 297789 by mananth(12270)   on 2011-03-28 21:11:49 (Show Source): You can put this solution on YOUR website!x+4y=40 .............1 x+2y=11 .............2 multiply (1)by 1 Multiply (2) by -2 x+4y=40 -2x-4y=-22 Add the two equations x=-18 plug value ofxin (1) x+4y=40 -18+4y=40 4y=40+18 4y=58 y=14.50
 Mixture_Word_Problems/428386: how much pure gold (24k) must be mixed with 60% gold to get 20 grams of 75% gold1 solutions Answer 297786 by mananth(12270)   on 2011-03-28 21:03:25 (Show Source): You can put this solution on YOUR website!......... percent ---------------- quantity 24k 100---------------- x gms Gold 60% 60---------------- 20-x gms Total 75.00% ---------------- 20 100x+60(20-x)=75*20 100x+1200-60x=1500 100x-60x =1500-1200 40x=300 /40 x=7.5gms
 Linear-equations/428412: equation for the line that passes through the point (-1, 2) and is parallel to the line with equation 2y+6x=101 solutions Answer 297783 by mananth(12270)   on 2011-03-28 20:50:53 (Show Source): You can put this solution on YOUR website!6x+2y=10 Find the slope of this line 2 y=-6x+10 Divide by 2 y =-3x+ 5 Compare this equation with y=mx+b slope m =-3 The slope of a line parallel to the above line will be the same The slope of the required line will be -3 m=-3,point(-1,2 ) Find b by plugging the values of m & the point in y=mx+b 2=3.00+ b b=-1 m=-3 Plug value of the slope and b The required equation is y=-3x-1 point (-1, 2) and is parallel to the line with equation 2y+6x=10
 Linear-equations/428398: bob has 60 coins consisting of quarters and dimes. The coins combined value is \$9.45. Find out how many are quarters and how many are dimes1 solutions Answer 297781 by mananth(12270)   on 2011-03-28 20:43:31 (Show Source): You can put this solution on YOUR website! quarters ------------ x dimes ------------ y 1 x + 1 y = 60 .............1 25 x + 10 y = 945 .............2 multiply (1)by -10 Multiply (2) by 1 -10 x + -10 y = -600 25 x + 10 y = 945 Add the two equations 15 x=345 /15 x=23 quarters plug value of x in (1) x+y=60 23+y=60 y = 60 + -23 y = 37 dimes
 Miscellaneous_Word_Problems/428106: The speed of a stream is 3 mph. A boat travels 5 miles upstream in the same time it takes to travel 11 miles downstream. What is the speed of the boat in still water? Any insight please.1 solutions Answer 297624 by mananth(12270)   on 2011-03-28 11:05:07 (Show Source): You can put this solution on YOUR website!boat speed x mph current speed 3 mph .. against current x - 3 mph with current x + 3 mph Distance upstream= 5 Distance downstream= 11 Time = same 5 /(x- 3 )= 11 /(x+ 3 ) 5 *(x+ 3 )= 11 *(x- 3 ) 5 x + 15 = 11 x -33 11 x -5 x = 33 + 15 6 x = 48 / 6 x= 8 mph
 percentage/428076: Hi, I need your help on this question: In a fish shop,60% of the fish were guppies and the rest were angelfish. After 81 fishes were removed, the number of guppies decreased by 25% and the number of angelfish was 1/4 of the original number of angelfish. a)How many guppies were removed? b)How many angelfish were there at first? Thank you, I really appreciate your help! 1 solutions Answer 297623 by mananth(12270)   on 2011-03-28 10:54:11 (Show Source): You can put this solution on YOUR website!In a fish shop,60% of the fish were guppies and the rest were angelfish. After 81 fishes were removed, the number of guppies decreased by 25% and the number of angelfish was 1/4 of the original number of angelfish. a)How many guppies were removed? b)How many angelfish were there at first? Thank you, I really appreciate your help! let total fish be x 0.6x = guppies 0.4x = angelfish .. x-81 = 0.75*0.6x +0,25*0.4x x-81=0.45x+0.1x x-81=0.55x 0.45x=81 x=180 fish 60 % of 180 = 108 were guppies 40%of 180= 72 were angel fish ... 25%of 108 = 27 guppies were removed
 Money_Word_Problems/428064: When Sara Whitehorse changed jobs, she rolled over the \$7700.00 in her retirement account into two simple interest accounts. On one account, the annual simple interest rate is 8%, and on the second account, the annual simple interest is 6%. How much must be invested in each account if the two accounts earned the same amount of annual interest? 1 solutions Answer 297610 by mananth(12270)   on 2011-03-28 09:33:15 (Show Source): You can put this solution on YOUR website!\$x at 8% 7700-x at6% 6(7700-x)=8x 46200-6x=8x 14x=46200 /14 x=46200/14 x=3300 \$3300 at 8% Balance at6%
 Polynomials-and-rational-expressions/428065: please help factor and show how you checked it x^2+1=2x I think the answer is (x+1)^2 but I don't know how to show my work and also don't know how to show Check process.1 solutions Answer 297605 by mananth(12270)   on 2011-03-28 09:26:33 (Show Source): You can put this solution on YOUR website!x^2+1=2x x^2-2x+1=0 x^2-x-x+1=0 x(x-1)-1(x-1)=0 (x-1)(x-1)=0 (x-1)^2=0
 Travel_Word_Problems/428027: An airplane flew for 6 hours at a speed of 455 miles per hour and then for 5 more hours at a speed of x miles per hour. The average speed of the airplane was 495 miles per hour. Write an equation that could be used to find x.1 solutions Answer 297604 by mananth(12270)   on 2011-03-28 09:23:41 (Show Source): You can put this solution on YOUR website!6 hours at 455 mph = 2730 miles 5 hours at x mph distance = 5x .. Total distance = 5x+2730 Total time = 11 hours Average speed = (5x+2730)/11 mph 495 = (5x+2730)/11 495*11= 5x+2730 5x=5445-2730 5x=2715 x=543
 Expressions-with-variables/428063: I am supposed to solve using the substitution method. 5x-6y=-20 5x+45=y Here is what I have tried and I think it is wrong. I switched the 2nd equation so that it read y=5x+45. It was then, 5x-6y=-20 y=5x+45 Here is how I worked it out 5x-6(5x+45)=-20 5x-30x-270=-20 -35x-270+270=-20+270 -35x=250 and I divided both sides by -35 and got 7.14 but I know this is wrong and I do not know where or what I did wrong. 1 solutions Answer 297601 by mananth(12270)   on 2011-03-28 09:01:42 (Show Source): You can put this solution on YOUR website!5x-6y=-20 5x+45=y 5x-6y=-20 .............1 y=45+5x ---------2 plug the value of y in (1) 5x-6(45+ 5x)=-20 5x-270-30x=-20 5x-30x=-20+270 -25x=250 /-25 x=-10 Plug the value of x in (1) 5x-6y=-20 5*-10-6y =-20 -50-6y=-20 -6y=30 /-6 y=-5 CHECK y=45+5x -5=45-50
 Trigonometry-basics/428039: two masts are 20 m and 12 m high.if the line joining their tops make an angle of 35 degree with the horizontal find their distance apart1 solutions Answer 297583 by mananth(12270)   on 2011-03-28 05:27:57 (Show Source): You can put this solution on YOUR website!the difference in height = 8 m Tan 35 = height/base base = 8/Tan 35 distance = 11.42 m
 Numbers_Word_Problems/427991: Two numbers are in the ratio 1:3. If i add 2 to each of the numbers, the ratio becomes 1:2. Find the number. PLease write it in the form of algebraic equation. Thank You!1 solutions Answer 297581 by mananth(12270)   on 2011-03-28 04:44:40 (Show Source): You can put this solution on YOUR website!Let one number be x let other number be y x/y = 1/3 cross multiply 3 x = 1 y 3x -y =0 ...........1 ( X +2)/(y+2)= ½ 2(x+2)= 1(y+2)2x+4=y+2 2x-y=-2 ............2 Multiply (1) by -1 we get -3x-y=0 ............3 Add (3)&(2) -x=-2 x=2 2 & 6
 Miscellaneous_Word_Problems/428009: The speed of a stream is 5mph. A boat travels 5 miles upstream in the same time it takes to travel 15 miles downstream. What is the speed of the boat in still water. help please.1 solutions Answer 297580 by mananth(12270)   on 2011-03-28 04:40:04 (Show Source): You can put this solution on YOUR website!boat speed x mph current speed 5 mph .. against current x - 5 mph with current x + 5 mph Distance against current 5 Distance with current 15 Time = same 5 /(x- 3 )= 15 /(x+ 3 ) 5 *(x+ 3 )= 15 *(x- 3 ) 5 x + 15 = 15 x -45 15 x -5 x = 45 + 15 10 x = 60 / 10 x= 6 mph
 Miscellaneous_Word_Problems/428014: A plane flies 435 miles with the wind and 345 miles against the wind in the same length of time. If the speed of the wind is 15mph, find the speed of the plane in still air.1 solutions Answer 297579 by mananth(12270)   on 2011-03-28 04:34:20 (Show Source): You can put this solution on YOUR website!let speed in still air be x mph wind speed 10 mph .. against wind x - 10 mph with wind x + 10 mph Distance against wind 345 Distance with tail wind 435 Time = same 345 /(x- 3 )= 435 /(x+ 3 ) 345 *(x+ 3 )= 435 *(x- 3 ) 345 x + 1035 = 435 x -1305 435 x -345 x = 1305 + 1035 90 x = 2340 / 90 x= 26 mph
 Linear_Equations_And_Systems_Word_Problems/428026: A scientist has one alloy containing 39% copper and another containing 61% copper. How many pounds of each alloy must he use to make 41 pounds of a third alloy containing 48% copper?1 solutions Answer 297577 by mananth(12270)   on 2011-03-28 04:20:13 (Show Source): You can put this solution on YOUR website!.........percent ---------------- quantity Alloy 1 39 ---------------- x pounds Alloy 2 61 ---------------- 41-x pounds Total 48% ---------------- 41 39x+61(41-x)=48* 41 39x+2501 -61x=1968 39x-61x= 1968-2501 -22x=-533 /-22 x=24.23 pounds 39.00% 16.77 pounds 61.00%
 Travel_Word_Problems/428032: A pilot flies 500 miles against a 20-mile-per-hour wind. On the next day, the pilot flies back home with a 10-mile-per-hour tail wind. The total trip (both ways) takes 4 hours. Find the speed of the airplane without a wind.1 solutions Answer 297574 by mananth(12270)   on 2011-03-28 04:12:56 (Show Source): You can put this solution on YOUR website!plane speed in still air x wind speed 20 against wind x- 10 with wind x+10 Distance= 500 miles Time agianst + time with wind =4 hours t=d/r 500/(x+20)+500/(x-20)= 4 LCD = (x-20)(x +20) 500*(x-20)+500(x+20)=4 500x-10000+500x+10000=4x ^2-400 1000x=4x ^2-400 4x^2-1000x-400=0 Find the roots of the equation by quadratic formula a= 4 b= -1000 c= -400 b^2-4ac= 1000000 - 6400 b^2-4ac= 1006400 x1=(1000+1003.19 )/8 x1= 250.4 mph x2=(1000-1003.19) /8 x2=-0.4 Ignore negative value 250.4 mph =speed in still air
 Mixture_Word_Problems/427993: A silversmith mixed 25 g of a 60% silver alloy with 40 g of a 5% silver alloy. What is the percent concentration of the resulting alloy? (Round to the nearest tenth of a percent.) %1 solutions Answer 297555 by mananth(12270)   on 2011-03-27 23:29:26 (Show Source): You can put this solution on YOUR website! percent ---------------- quantity alloy 60 ---------------- 25 gms alloy 5 ---------------- 40 gms Total x ---------------- 65 gms 60*25+5* 40=65x 1500+200 =65x 1700=65x /65 1700/65= x 26.15=x 26.5% mix
 Length-and-distance/427989: it takes a passenger train 5 hr less time than it takes a freight train to make the trip from hughesville to rockville. the passenger train averages 105km/h while the freight train averages 70 km/h find the distance from rockville to hughesville.1 solutions Answer 297552 by mananth(12270)   on 2011-03-27 23:18:07 (Show Source): You can put this solution on YOUR website!the trip from hughesville to rockville. the passenger train averages 105km/h while the freight train averages 70 km/h find the distance from rockville to hughesville. distance = x time freight train = x/70 time passenger train = x/105 x/70-x/105 = 5 LCD = 7350 105x-70x= 7350*5 35x=36750 /35 x=36750/35 x= 1050 km
 Linear-systems/427984: 0.1x+0.7y=-2.3 0.3x-0.2y=2.3 solve the system using substitution method1 solutions Answer 297547 by mananth(12270)   on 2011-03-27 23:02:44 (Show Source): You can put this solution on YOUR website!0.1x+0.7y=-2.3 0.3x-0.2y=2.3 multiply both equations by 10 x+7y=-23 3x-2y=23 x+7y=-23 .............1 -2y=23-3 x---------2 /-2 y=-11.5- 1.5x Plug the value of y in (1) x+7(-11.5+1.5x)= -23 x-80.5+10.5x)=-23 x+10.5x= -23 11.5x=57.5 /11.5 x=5 Plug the value of x in (1) x+7y=-23 5+7y=-23 5+7y=-23 7y=-28 /7 y=-4
 Travel_Word_Problems/427544: the speed of a stream is 3 mph. A boat travels 3 miles upstream in the same time it takes to travel 9 miles downstream. What is the speed of the boat in still water? 1 solutions Answer 297383 by mananth(12270)   on 2011-03-27 09:32:44 (Show Source): You can put this solution on YOUR website!let speed in still water = x mph current speed 3 mph .. upstream speed = x-3 mph downstream speed = x+3 mph Distance upstream=3 Distance downstream=9 Time = same 3/(x-3)= 9/(x+3) 3*(x+3)= 9*(x-3) 3x+3=9x-27 9x-3x=27 +3 6x=30 /6 x=5mph
 Travel_Word_Problems/427609: a biker can travel at a speed of x km/h over a distance of 15km. if the biker reduces his speed by 2km/h he will only manage to travel 10km for the same time Calculate x1 solutions Answer 297374 by mananth(12270)   on 2011-03-27 09:09:20 (Show Source): You can put this solution on YOUR website!t=d/r t = same 15/x= 12/x-2 15(x-2)=12x 15x-30=12x 15x-12x=30 3x=30 x=10
 Rational-functions/427563: Please help me set up this problem: "Tim paddled his kayak 12 km upstream against a 3 km/hour current and back again in 5 hours and 20 minutes. In that time how far could he have paddled in still water?"1 solutions Answer 297365 by mananth(12270)   on 2011-03-27 08:21:31 (Show Source): You can put this solution on YOUR website! speed in still water = r current speed =3 upstream speed = r-3 downstream speed = r+3 Distance= 12 miles Time upstream + time downstream = 5.33 hours 12/(r+3) +12/(r-3 )=5.33 LCD = (r-3)(r+ 3) 12*(r-3) +12(r+3 )= 5.33 12r-36r+12r+36=5.33 r^2-24r=5.33r^2-47.97 5.33r^2- 24r-47.97 Find the roots of the equation by quadratic formula a=5.33 b=-24 c=-47.97 b^2-4ac= 576+1022.72 b^2-4ac= 1598.72 x1=(24+ 39.98)/ 10.66 x1= 6 x2=(24-39.98) /10.66 x2= -1.5 ( ignore) Speed = 6 mph