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 'nerdybill'

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, >>Next

 Mixture_Word_Problems/585310: Vince need 12 quarts of a 60% anti-freeze solution. He will continue an amount of 100% anti-freeze with an amount of a 50% anti-freeze solution. How many quarts of each solution should be mixed to make the required amount of the 60% anti-freeze solution?1 solutions Answer 373271 by nerdybill(6963)   on 2012-03-11 09:02:10 (Show Source): You can put this solution on YOUR website! Vince need 12 quarts of a 60% anti-freeze solution. He will continue an amount of 100% anti-freeze with an amount of a 50% anti-freeze solution. How many quarts of each solution should be mixed to make the required amount of the 60% anti-freeze solution? . Let x = amount (quarts) of 100% solution then 12-x = amount (quarts) of 50% solution . x + .50(12-x) = .60(12) x + 6-.50x = 7.2 .50x + 6 = 7.2 .50x = 1.2 x = 2.4 quarts of 100% solution . 50% solution: 12-x = 12-2.4 = 9.6 quarts of 50% solution
 Square-cubic-other-roots/585317: compute m that satisfies 8^m=32?1 solutions Answer 373269 by nerdybill(6963)   on 2012-03-11 08:56:17 (Show Source):
 Exponential-and-logarithmic-functions/584812: 2 log 5 + log x=21 solutions Answer 372903 by nerdybill(6963)   on 2012-03-09 11:54:53 (Show Source): You can put this solution on YOUR website!2 log 5 + log x=2 log 5^2 + log x=2 log 25 + log x=2 log 25x = 2 25x = 10^2 25x = 100 x = 4
 logarithm/584768: what is the answer to log 3z equal 2 ? what is the answer to ln x equal 2 ? whats the answer to 3 ln 5x equal 10 ? whats the answer to ln square root x-8 equal 5 ?1 solutions Answer 372873 by nerdybill(6963)   on 2012-03-09 09:06:20 (Show Source): You can put this solution on YOUR website!what is the answer to log 3z equal 2 ? . what is the answer to ln x equal 2 ? . whats the answer to 3 ln 5x equal 10 ? . whats the answer to ln square root x-8 equal 5 ?
 Surface-area/584762: The area of the piece is 30 ft². The length is 1 less than 3 times the width. How wide should the metal piece be? Round to the nearest hundredth of a foot.1 solutions Answer 372871 by nerdybill(6963)   on 2012-03-09 09:00:00 (Show Source): You can put this solution on YOUR website! The area of the piece is 30 ft². The length is 1 less than 3 times the width. How wide should the metal piece be? Round to the nearest hundredth of a foot. . Let w = width then 3w-1 = length . w(3w-1) = 30 3w^2-w = 30 3w^2-w-30 = 0 replace middle term: 3w^2 +9w-10w -30 = 0 group terms: (3w^2+9w) - (10w+30) = 0 3w(w+3) - 10(w+3) = 0 (w+3)(3w-10) = 0 w = {-3, 10/3} throw out the negative solution (extraneous) leaving: w = 10/3 w = 3.33 feet
 Triangles/584754: what is the length of the hypotenuse of a right triangle that has legs with lengths of 5 and 4?1 solutions Answer 372869 by nerdybill(6963)   on 2012-03-09 08:55:46 (Show Source): You can put this solution on YOUR website!what is the length of the hypotenuse of a right triangle that has legs with lengths of 5 and 4? apply the Pythagorean Theorem: Let h = hypotenuse then h^2 = 5^2 + 4^2 h^2 = 25 + 16 h^2 = 41 h = sqrt(41) h = 6.40
 Miscellaneous_Word_Problems/584564: Li's car gets 23 miles per gallon on the highway. If 1 gallon of gas cost #3.20, and Li has \$50.00 worth of gas in her car, how many miles can she drive on the highway? Give the exact answer.1 solutions Answer 372812 by nerdybill(6963)   on 2012-03-08 20:57:57 (Show Source): You can put this solution on YOUR website! Li's car gets 23 miles per gallon on the highway. If 1 gallon of gas cost #3.20, and Li has \$50.00 worth of gas in her car, how many miles can she drive on the highway? Give the exact answer. 50/3.20 *23 500/32 *23 125/8 *23 2875/8 359 and 3/8 miles (exact answer)
 Rate-of-work-word-problems/584389: It takes 9 hours for pump A to fill a tank alone. Pump B takes 15 hours to fill the same tank alone. If pumps A,B, and C are used, the tank fills in 5 hours. How long does it take pump C to fill the tank?1 solutions Answer 372780 by nerdybill(6963)   on 2012-03-08 16:51:59 (Show Source): You can put this solution on YOUR website! It takes 9 hours for pump A to fill a tank alone. Pump B takes 15 hours to fill the same tank alone. If pumps A,B, and C are used, the tank fills in 5 hours. How long does it take pump C to fill the tank? . Let c = time (hours) it takes for pump C to fill tank then 5(1/9 + 1/15 + 1/c) = 1 5/9 + 5/15 + 5/c = 1 5/9 + 1/3 + 5/c = 1 multiplying both sides by 9c: 5c + 3c + 45 = 9c 8c + 45 = 9c 45 hours = c
 Linear-equations/584418: Which of the following is equivalent to -3(y+7)? A. -3y+7 B. -3y-21 C. -21+y1 solutions Answer 372778 by nerdybill(6963)   on 2012-03-08 16:47:45 (Show Source): You can put this solution on YOUR website!-3(y+7) distribute the -3 to each term inside the parenthesis: -3y-21 answer, then, is B
 test/584414: I need to know how to factor a polynomial. The problem I have is 8m - 6 . Please reply soon. 1 solutions Answer 372777 by nerdybill(6963)   on 2012-03-08 16:46:16 (Show Source): You can put this solution on YOUR website!8m - 6 has 2 terms: 8m and 6 factoring using prime factors we get: 8m = 2*2*2*m 6 = 2*3 a "common factor" is 2, so: 2(4m - 3) (this is what they're looking for)
 Triangles/584202: is it possible to construct a triangle with side lengths 10,11, and 201 solutions Answer 372720 by nerdybill(6963)   on 2012-03-08 09:41:53 (Show Source): You can put this solution on YOUR website!10,11, and 20 let's assign: 10(a),11(b), and 20(c) . The triangle inequality rule says that: c – b < a < c + b 20 – 11 < 10 < 20 + 11 9 < 10 < 31 Since the above is TRUE: answer: YES, it is possible
 Rectangles/583565: If the length of a rectangle is 15 cm and the width is 12 cm, what is the area?1 solutions Answer 372513 by nerdybill(6963)   on 2012-03-07 09:34:58 (Show Source): You can put this solution on YOUR website! If the length of a rectangle is 15 cm and the width is 12 cm, what is the area? For any rectangle: area = width * length area = 12*15 area = 180 square cm
 Radicals/583584: 1 solutions Answer 372512 by nerdybill(6963)   on 2012-03-07 09:32:59 (Show Source):
 Linear-systems/583570: A biologist has a 30% solution and a 5% solution of the same plant nutrient. How many cubic centimeters (cc) of each solution should be mixed to obtain a 25 cc of a 25% solution? (Round your answers to 2 decimal places if needed)1 solutions Answer 372510 by nerdybill(6963)   on 2012-03-07 09:28:08 (Show Source): You can put this solution on YOUR website! A biologist has a 30% solution and a 5% solution of the same plant nutrient. How many cubic centimeters (cc) of each solution should be mixed to obtain a 25 cc of a 25% solution? (Round your answers to 2 decimal places if needed) . Let x = amount (cc) of 30% solution then 25-x = amount (cc) of 5% solution . .30x + .05(25-x) = .25(25) .30x + 1.25-.05x = 6.25 .25x + 1.25 = 6.25 .25x = 5 x = 20 cc (of 30% solution) . amount of 5% solution: 25-x = 25-20 = 5 cc
 Mixture_Word_Problems/583572: A 20% iodine solution is mixed with a 70% iodine solution to produce 5 gallons of 50% Iodine solution. How many gallons of each solution are needed?1 solutions Answer 372507 by nerdybill(6963)   on 2012-03-07 09:22:25 (Show Source): You can put this solution on YOUR website! A 20% iodine solution is mixed with a 70% iodine solution to produce 5 gallons of 50% Iodine solution. How many gallons of each solution are needed? . Let x = amount (gallons) of 20% solution then 5-x = amount (gallons) of 70% solution . .20x + .70(5-x) = .50(5) .20x + 3.5-.70x = 2.5 3.5-.50x = 2.5 -.50x = -1 x = -1/(-.50) x = 2 gallons (of 20% solution) . 70% solution: 5-x = 5-2 = 3 gallons
 logarithm/583440: what does x equal when (2/5)^x=7?1 solutions Answer 372447 by nerdybill(6963)   on 2012-03-06 21:52:42 (Show Source):
 Rectangles/582980: The perimeter of square is 40m. The perimeter of rectangle of length 12m is as the same as the perimeter of square. Find which encloses the greater area square or rectangle?1 solutions Answer 372271 by nerdybill(6963)   on 2012-03-06 08:42:19 (Show Source): You can put this solution on YOUR website! The perimeter of square is 40m. The perimeter of rectangle of length 12m is as the same as the perimeter of square. Find which encloses the greater area square or rectangle? Square: since all four sides are equal: 40/4 = 10 m (length of one side) area = 10*10 = 100 sq m . Rectangle: Let w = width then 2(w+12) = 40 w+12 = 20 w = 8 m Area = 8*12 = 96 sq m . Answer: the square
 Exponential-and-logarithmic-functions/582895: Solve log5x+log10=0. Round to the nearest hundredth if necessary. This what I have tired: log5(x+2)=0 10^log5(x+2)= 10^0 5x+10=1 I wasn't sure what to do next and if I was doing the problem correctly.1 solutions Answer 372264 by nerdybill(6963)   on 2012-03-06 01:32:38 (Show Source): You can put this solution on YOUR website!log5x+log10=0 log5x(10)=0 log50x=0 50x=10^0 50x=1 x = 1/50 x = 0.02
 real-numbers/582275: AMY CAN CLEAN THE ELEPHANT ENCLOSURE IN 4 HOURS, BUT IT TAKE JOEL 6 HOURS. HOW LONG WOULD IT TAKE THEM WORKING TOGETHER.....PLEASE HELP1 solutions Answer 372010 by nerdybill(6963)   on 2012-03-05 00:47:33 (Show Source): You can put this solution on YOUR website! AMY CAN CLEAN THE ELEPHANT ENCLOSURE IN 4 HOURS, BUT IT TAKE JOEL 6 HOURS. HOW LONG WOULD IT TAKE THEM WORKING TOGETHER.....PLEASE HELP . Let x = time (hours) it takes together then x(1/4 + 1/6) = 1 multiplying both sides by 12: x(3 + 2) = 12 x(5) = 12 x = 12/5 x = 2.4 hours or x = 2 hours and 24 minutes
 Proportions/581812: Translate the following statement into an equation. Seven less then twice a number is 4 more than the number1 solutions Answer 371817 by nerdybill(6963)   on 2012-03-04 10:19:05 (Show Source): You can put this solution on YOUR website! Translate the following statement into an equation. Seven less then twice a number is 4 more than the number . Let n = the number then 2n-7 = n+4
 Equations/581820: Could you please help me solve this equation? I keep coming up with answers other than the one that the book shows is right! Could you please show the steps you took to arrive at the answer? Thanks!!! (1/2 is one half - couldn't get it to show another way) 1/2(2n-5)=4n-11 solutions Answer 371816 by nerdybill(6963)   on 2012-03-04 10:17:21 (Show Source): You can put this solution on YOUR website!1/2(2n-5)=4n-1 multiplying both sides by 2: (2n-5)=8n-2 2n-5=8n-2 subtracting 2n from both sides: -5=6n-2 adding two to both sides: -3=6n dividing both sides by 6: -3/6 = n -1/2 = n
 Miscellaneous_Word_Problems/581770: Liam thinks of a number. He multiplies the number by 5 and then subtracts 60 from the result . His answer equals the number he started with . What was the number Liam started with ?1 solutions Answer 371805 by nerdybill(6963)   on 2012-03-04 05:17:38 (Show Source): You can put this solution on YOUR website!Liam thinks of a number. He multiplies the number by 5 and then subtracts 60 from the result . His answer equals the number he started with . . Let x = number Liam started with then 5x-60 = x 5x = x+60 4x = 60 x = 60/4 x = 15 . What was the number Liam started with ? 15
 Rectangles/581757: what is the dimension of a rectangle whose length is 5 less than twice its width and whose area is 63 square units?1 solutions Answer 371804 by nerdybill(6963)   on 2012-03-04 05:15:37 (Show Source): You can put this solution on YOUR website! what is the dimension of a rectangle whose length is 5 less than twice its width and whose area is 63 square units? . Let w = width then from: "length is 5 less than twice its width" we get 2w-5 = length . since: area = width * length 63 = w(2w-5) 63 = 2w^2-5w 0 = 2w^2-5w-63 rewrite the middle term as: 0 = 2w^2-14w+9w-63 group: 0 = (2w^2-14w) + (9w-63) 0 = 2w(w-7) + 9(w-7) 0 = (w-7)(2w+9) w = {-9/2, 7} toss out the negative term (extraneous) leaving: w = 7 units (width) . Length: 2w-5 = 2(7)-5 = 14-5 = 9 units . Dimension: 7 units by 9 units
 percentage/581768: After 10% discount has been given the discounted cost of a coat is \$765. What was the original cost of the coat? how do i work this out?1 solutions Answer 371803 by nerdybill(6963)   on 2012-03-04 05:08:00 (Show Source): You can put this solution on YOUR website!After 10% discount has been given the discounted cost of a coat is \$765. What was the original cost of the coat? . Let x = original cost of coat then x - .10x = 765 x(1 - .10) = 765 x(.90) = 765 x = 765/.90 x = \$850
 Exponential-and-logarithmic-functions/581754: This is the question: log(base 5) 125^1/2 + log(base 11) 121^1/3= 13/6 What I tried: log(base 5) 125^1/2 + log(base 11) 121^1/3 = 13/6 log(base 5) 5*5^1/2+ log (base11) 121^1/3= 13/6 Yup,unfortunately, I'm stuck at here. Thanks in advance ^0^!!1 solutions Answer 371802 by nerdybill(6963)   on 2012-03-04 05:04:24 (Show Source): You can put this solution on YOUR website!log(base 5) 125^1/2 + log(base 11) 121^1/3= 13/6 log(base 5) (5^3)^1/2 + log(base 11) (11^2)^1/3= 13/6 log(base 5) (5^3/2) + log(base 11) (11^2/3)= 13/6 3/2 + 2/3= 13/6 9/6 + 4/6= 13/6 13/6 = 13/6
 logarithm/581756: 3. Find all real solutions to the following: a) log2(x - 2) + log2(x + 1) = log2 101 solutions Answer 371800 by nerdybill(6963)   on 2012-03-04 04:59:29 (Show Source): You can put this solution on YOUR website!log2(x - 2) + log2(x + 1) = log2 10 log2(x - 2)(x + 1) = log2 10 (x - 2)(x + 1) = 10 x^2+x-2x-2 = 10 x^2-x-2 = 10 x^2-x-12 = 0 (x-4)(x+3) = 0 x = {-3, 4} The -3 is an "extraneous" solution so we throw it out leaving: x = 4
 Exponential-and-logarithmic-functions/581664: The question is: log x^3 - 2log 1/x - 1= 0 What I tried: 3log x- (-2log x) - 1= 0 3log x + 2 log x - 1= 0 5 log x- 1 = 0 5 log x = 1 log x = 1/5 x= 10^1/5 or 3log x- (-2log x) - 1= 0 3log x + 2 log x - 1= 0 5 log x- 1 = 0 5 log x = 1 log x^5 = 1 x^1=5 x=5 I'm still confused with this kind of questions. Thanks in advance ^0^! 1 solutions Answer 371783 by nerdybill(6963)   on 2012-03-03 21:17:33 (Show Source): You can put this solution on YOUR website!log x^3 - 2log 1/x - 1= 0 log x^3 - 2log 1/x = 1 log x^3 - log (1/x)^2 = 1 log x^3 - log (1/x^2) = 1 log x^3 - log (x^-2) = 1 log x^3/(x^-2) = 1 log x^3x^2 = 1 log x^5 = 1 x^5 = 10^1 x^5 = 10 x = 10^(1/5) x = 1.5849
 logarithm/581589: How do I solve the following using the relationship between natural logarithms, Ins, and the number e? 1)In(2m+3)=8 2)1.1+In x^2=6 3)e^x+1=301 solutions Answer 371714 by nerdybill(6963)   on 2012-03-03 16:45:15 (Show Source): You can put this solution on YOUR website!1)In(2m+3)=8 2m+3 = e^8 2m = e^8 - 3 m = (e^8 - 3)/2 m = 1488.98 . 2)1.1+In x^2=6 Ln x^2 = 6 - 1.1 x^2 = e^(6 - 1.1) x = sqrt(e^(6 - 1.1)) x = 11.59 . 3)e^x+1=30 e^x=30-1 x = ln(30-1) x = 3.37
 logarithm/581575: How do I write these equations in logarithmic form 3^5=243 , g^f=v , x^3y=51 solutions Answer 371709 by nerdybill(6963)   on 2012-03-03 16:01:16 (Show Source): You can put this solution on YOUR website!Apply "log rules": . .
 Mixture_Word_Problems/581415: Okay I'm stumped on this problem. I have tried to figure out the equation but I keep geting stuck. The problem is: "A chemist has a 90% solution of sulfuric acid and a 70% solution of the same acid. How many gallons of each must be mixed in order to make 200 gallons of 75% solution?" Here's what I know: I know that x is the amount of the 90% solution and that y would be the amount of the 70% solution. I think that the equation would be .90x + .70y = .75 and that the other equation is x+y=200. but I am not sure I did that right and I keep getting fractions as my answer. Help please.1 solutions Answer 371664 by nerdybill(6963)   on 2012-03-03 09:10:53 (Show Source): You can put this solution on YOUR website!Okay I'm stumped on this problem. I have tried to figure out the equation but I keep geting stuck. The problem is: "A chemist has a 90% solution of sulfuric acid and a 70% solution of the same acid. How many gallons of each must be mixed in order to make 200 gallons of 75% solution?" Here's what I know: I know that x is the amount of the 90% solution and that y would be the amount of the 70% solution. I think that the equation would be .90x + .70y = .75 and that the other equation is x+y=200. but I am not sure I did that right and I keep getting fractions as my answer. Help please. . You almost had it right. It should have been: Let x = amount (gallons) of 90% solution and y = amount (gallons) of 70% solution . x+y=200 (equation 1) .90x + .70y = .75(200) (equation 2) . Solving equation 1 for y x+y=200 y=200-x Substitute above into equation 2: .90x + .70y = .75(200) .90x + .70(200-x) = .75(200) .90x + 140-.70x = 150 .20x + 140 = 150 .20x = 10 x = 50 gallons (of 90% solution) . 70% solution: x+y=200 50+y=200 y = 150 gallons
 Polynomials-and-rational-expressions/581420: h=-16t^2+vt+s, where h is the height (in feet), t is the time in motion (in seconds), v is the initial velocity (in feet per second), and s is the initial height(in feet) A gymnast dismounts the uneven parallel bars at a height of 8 feet with an initial upward velocity of 8 feet per second. Find the time (in seconds) it takes for the gymnast to reach the ground. 1 solutions Answer 371661 by nerdybill(6963)   on 2012-03-03 09:01:05 (Show Source): You can put this solution on YOUR website!h=-16t^2+vt+s, where h is the height (in feet), t is the time in motion (in seconds), v is the initial velocity (in feet per second), and s is the initial height(in feet) A gymnast dismounts the uneven parallel bars at a height of 8 feet with an initial upward velocity of 8 feet per second. Find the time (in seconds) it takes for the gymnast to reach the ground. . from the statement of the problem we have: v is 8 ft per sec s is 8 ft set h to zero (ground) and solve for t: h=-16t^2+vt+s 0=-16t^2+8t+8 dividing both sides by 8: 0=-2t^2+t+1 multiplying both sides by -1: 0=2t^2-t-1 0=2t^2-2t+t-1 0=(2t^2-2t)+(t-1) 0=2t(t-1)+(t-1) 0=(t-1)(2t+1) t = {-1/2, 1} throw out the negative solution leaving: t = 1 second