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# Recent problems solved by 'josmiceli'

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 Travel_Word_Problems/746609: If Micheal's car can travel 28 miles with one gallon of gas how many miles can he travel with 16 gallons of gas? 1 solutions Answer 454391 by josmiceli(9819)   on 2013-05-08 20:47:31 (Show Source): You can put this solution on YOUR website! Multiply both sides by he can travel 448 miles
 Rate-of-work-word-problems/746597: Can you help please! One pipe can fill a tank in 4 hours. A second pipe can fill it in 5 hours. A third pipe can fill it in 6 hours. How long would it take all three pipes to fill the tank working together?1 solutions Answer 454389 by josmiceli(9819)   on 2013-05-08 20:42:48 (Show Source): You can put this solution on YOUR website!Add their rates of filling 1st pipe: ( 1 tank filled ) / ( 4 hrs ) 2nd pipe: ( 1 tank filled ) / ( 5 hrs ) 3rd pipe: ( 1 tank filled ) / ( 6 hrs ) -------------- Multiply both sides by hrs All 3 pipes working together take 1 hr and 37 min
 Rate-of-work-word-problems/746589: It takes one man 10 hours to do a certain job. After he has worked for 4 hours, another man is sent to help him. The two men complete the job in 4 hours. How long would it take the second man to do the entire job alone?1 solutions Answer 454385 by josmiceli(9819)   on 2013-05-08 20:32:31 (Show Source): You can put this solution on YOUR website!Add their rates of working to get their rate working together 1st man's rate: ( 1 job ) / ( 10 hrs ) Both men working together: ( 1 job ) / ( 4 hrs ) ------------ Let = the time in hours for the 2nd man to do the job alone ------------ Multiply both sides by hrs min It takes the 2nd man 6 hrs and 40 min to do the job alone
 Systems-of-equations/746575: please help me solve about system of two equation : 2x-y=10 x+5y=38 thank you so much 1 solutions Answer 454383 by josmiceli(9819)   on 2013-05-08 20:23:31 (Show Source): You can put this solution on YOUR website!(1) (2) Multiply both sides of (1) by (1) Now add the equations (1) (2) Divide both sides by ----------- Plug this result back into (2) (2) (2) (2) (2) ------------ the solutions are: ------------ check: (2) (2) OK You can check the other equation
 Unit_Conversion_Word_Problems/746387: If £6.40 is the. cost for meat weighing 1 kilo. How much money will I spend if the meat is 350 grams? Please tell me how to sort it out1 solutions Answer 454257 by josmiceli(9819)   on 2013-05-08 13:35:16 (Show Source): You can put this solution on YOUR website!The rate is in grams You will spend 2.24
 Travel_Word_Problems/746377: how long will it take for a 52 mph car take to catch up to a car at 26 mph if the car at 26 mph had a 2 hour head start 1 solutions Answer 454255 by josmiceli(9819)   on 2013-05-08 13:29:57 (Show Source): You can put this solution on YOUR website!In hrs, the slower car has a head start of mi Let = the distance the faster car goes until it catches the slower car. Start a stopwatch when the faster car leaves Let = the time on the stopwatch. Equation for faster car: (1) Equation for slower car: (2) ------------------- substitute (1) into (2) (2) (2) (2) It takes the faster car 2 hrs to catch the slower car check: (1) (1) (1) mi and (2) (2) (2) (2) mi OK
 Polynomials-and-rational-expressions/746361: Kareem purchased a leather jacket for \$800 with his new credit card. He budgeted \$50 a month to pay toward the debt. When he read the fine print on the credit card statement, he saw that for each month he owed a balance, a finance charge of \$17.50 would be added. If Kareem pays \$50 per month, how much money will the jacket actually cost?1 solutions Answer 454250 by josmiceli(9819)   on 2013-05-08 13:00:28 (Show Source): You can put this solution on YOUR website!Let = the number of monthly payments that he will make That will include interest. The last payment will not have a finance charge, since that will pay off the jacket. So, for payments, \$17.50 will be add on. That means will actually go towards the balance each month. The last month's payment will be \$50, all towards balance I can say: It looks like he could do it in 24 payments The last payment would have to be slightly more than \$50 The last payment would be \$52.50
 Mixture_Word_Problems/746115: How many pints of 1% peroxide solution should be mixed with 4% peroxide solution to obtain 10 pints of 2% peroxide solution?1 solutions Answer 454166 by josmiceli(9819)   on 2013-05-07 19:54:21 (Show Source): You can put this solution on YOUR website!Let = pints of 1% solution needed Let = pints of 4% solution needed = peroxide in 1% solution = peroxide in 4% solution -------------------------------- (1) (2) ----------------------------- (2) (2) Subtract (1) from (2) (2) (1) and, since (1) (1) (1) 6.667 pints of 1% solution are needed 3.333 pints of 4% solution are needed check: (2) (2) (2) (2) OK
 �t�e�s�t/746083: Hi Tutor, Can you please show me how to do the following question step by step. Question The sum of six times the first number and four times the second number is 48. If the product of two numbers is a maximum, what are the two numbers. So far I have the following: x= First number y= Second number 48= 6x+4y ---> x=48-4y/6 m=xy ---> m=48-4y/6 (y) Can you show me show to solve this step by step. Thanks.1 solutions Answer 454163 by josmiceli(9819)   on 2013-05-07 19:00:25 (Show Source): You can put this solution on YOUR website! Divide both sides by -------------------- This is a maximum at When , ------------ The numbers are 4 and 6 check: The 2 curves are and Here's the 2 plots along with the parabola that tells you the value of the product at the intersection.
 Exponents-negative-and-fractional/746098: please help me with this question, and i dont know if this problem is under the correct category sorry. "simplify each expression below. your answer should contain no parentheses and no negative exponents" 5t^-3 (five t negative cube)1 solutions Answer 454157 by josmiceli(9819)   on 2013-05-07 18:27:58 (Show Source): You can put this solution on YOUR website!You are in the right place Use the fact that
 Miscellaneous_Word_Problems/746051: Write an equation or inequality to solve this problem. Scott has \$30 to buy new baseball cards for his collection. He has chosen a Greg Maddux rookie card that costs \$8. What is the most he can spend on other baseball cards? 1 solutions Answer 454115 by josmiceli(9819)   on 2013-05-07 16:21:00 (Show Source): You can put this solution on YOUR website!Let = the most he can spend on other cards \$22 is the most he can spend
 Mixture_Word_Problems/746044: Arnold collects stamps and coins. The number of coins he has is 3 times more than half the number of stamps. If he has 51 stamps and coins altogether, how many stamps and coins does he have? I'm having trouble figuring out how to set up the equation.1 solutions Answer 454114 by josmiceli(9819)   on 2013-05-07 16:16:12 (Show Source): You can put this solution on YOUR website!Let = number of stamps he has Let = number of coins he has given: (1) (2) ----------------- Substitute (1) into (2) (2) Multiply both sides by (2) (2) ---------------- This doesn't work out to a whole number of stamps. I suspect that the problem should read: The number of coins he has is 3 more than half the number of stamps. and not The number of coins he has is 3 TIMES more than half the number of stamps. If that is so, (1) (2) Substitute (1) into (2) (2) (2) (2) (2) (2) and (2) (2) (2) He has 19 coins and 32 stamps
 Money_Word_Problems/746045: THREE INDIVIDUALS FORM A PARTNERSHIP AND AGREE TO DIVIDE THE PROFITS EQUALLY. X INVESTS \$9000, Y INVESTS \$7000, Z INVESTS \$4000. IF THE PROFITS ARE \$4800, HOW MUCH LESS DOES X RECEIVE THAN IF THE PROFITS WERE DIVIDED IN PROPORTION TO THE AMOUNT INVESTED? HOW DO YOU FIGURE THIS ANSWER? 1 solutions Answer 454113 by josmiceli(9819)   on 2013-05-07 16:03:21 (Show Source): You can put this solution on YOUR website!If the profit is divided equally, each gets \$1,600 -------------- The proportion of the amounts invested is: X : Y : Z = 9000 : 7000 : 4000 9000 : 7000 : 4000 = 9 :7 : 4 Now express the proportion as fractions of the sum 9 : 7 : 4 = 9/20 : 7/20 : 4/20 -------------------- X receives --------------- x receives \$560 less when profit is divided equally
 Rate-of-work-word-problems/746009: one pump can drain a pool in 7 minutes. When a second pump is also used together with the first, the pool only takes 3 minutes to drain. How long would it take the second pump to drain the pool if it were the only pump in use?1 solutions Answer 454107 by josmiceli(9819)   on 2013-05-07 14:58:41 (Show Source): You can put this solution on YOUR website!Add their rates of draining to get their rate of draining together ( 1 pool / 7 min ) + ( 1 pool / t min ) = ( 1 pool / 3 ) Solve for Multiply both sides by It will take the 2nd pump 5 min and 15 sec by itself
 Linear_Equations_And_Systems_Word_Problems/746010: In one week, Fearless Frank drove 100 miles on the freeway and 150 miles in town. His car consumed 18.2 gallons of gasoline. The next week his journeys took him over 180 miles of freeway and 30 miles of local driving, and he used only 10.9 gallons of gas. What were his highway m.p.g. and his local m.p.g.? 1 solutions Answer 454105 by josmiceli(9819)   on 2013-05-07 14:52:34 (Show Source): You can put this solution on YOUR website!The key is to see that ( miles driven ) / ( miles / gallon ) = gallons I can say: Let = mpg on the highway Let = mpg in town (1) (2) ----------------------------- (1) (2) ------------------------------ Multiply both sides of (2) by and subtract (1) from (2) (2) (1) and (2) (2) (2) (2) (2) ----------------- His highway m.p.g. was about 22 and his local m.p.g. was about 11 ----------------- check: (1) (1) (1) close enough
 Reduction-of-unit-multipliers/746011: a water hose can fill a 1 quart bottle with water in 2.2 seconds; I need to buy a pond pump but its flow rates are given in gallons per hour. what size pump should I purchase to the nearest 100 GPH?1 solutions Answer 454103 by josmiceli(9819)   on 2013-05-07 14:32:10 (Show Source): You can put this solution on YOUR website!You want an answer in ( gallons / hr ), so in terms of just units: ( quarts / sec ) x ( gallons / quart ) x ( sec / min ) x ( min / hr ) = ( gallons / hr ) ----------------------- This is easier to see if you pull out all the like units: ( quarts / quarts ) x ( sec/ sec ) x ( min / min ) x ( gallons / hr ) = ( gallons / hr ) ------------- Using your numbers: To the nearest 100 GPH, you need a 400 GPH pump
 Rate-of-work-word-problems/745788: Peter and Paul can do a certaion job in 3 hours. On a given day, they worked together for 1 hour then Paul left and Peter finishes the rest of the work in 8 more hours. How long will it take Peter to do the job alone?1 solutions Answer 454019 by josmiceli(9819)   on 2013-05-06 23:25:05 (Show Source): You can put this solution on YOUR website!If they can do the whole job in 3 hrs working together, then in 1 hour, they can do of the job That means there is 2/3 of the job left to do ----------------- Then, ( Peter's rate of working ) x ( 8 hrs ) = 2/3 Let = Peter's rate of working Peter would take 12 hrs to do the job alone check: ---------- Let = Paul's rate of working In hr, So, of the job is left Peter does OK
 Rate-of-work-word-problems/745794: father and a his son can dig a well if the father works 6 hours and his son works 12 hours or they can do its if the father works 9 hours and the son works 8 hours. How long will it take for the son to dig the well alone?1 solutions Answer 454007 by josmiceli(9819)   on 2013-05-06 22:10:56 (Show Source): You can put this solution on YOUR website!You can add their rates of digging to get their rate working together Let = father's rate of digging Let = Son's rate of digging -------------------------------- In general, I can say that: ( time spent digging ) x ( rate of digging ) = fraction of job done --------------- given: (1) (2) ( note that means entire job done ) ---------------- Multiply both sides of (1) by and both sides of (2) by Then subtract (2) from (1) ---------------------- (1) (2) ----------------- (1) (1) (1) (1) (1) (1) (1) (1) ----------------- The son would take 20 hrs working alone check: (2) (2) (2) (2) (2) OK
 Mixture_Word_Problems/745797: they combine 15lbs of a mix that is 60% peanuts with 10lbs of a second mix that is 30% peanuts. How many pounds of peanuts are in the combined mix? 1 solutions Answer 453996 by josmiceli(9819)   on 2013-05-06 21:32:49 (Show Source): You can put this solution on YOUR website! 12 pounds of peanuts are in the mix
 Travel_Word_Problems/745513: THE HEIGHT OF THE ROCKET AFTER t SECONDS WHEN FIRED STRAIGHT UP WITH AN INITIAL SPEED OF 150FT PER SECOND FROM AN INITIAL HEIGHT OF 2 CAN BE MODELED BY THE FUNCTION: s(t)=-16t^2+150t+2 WHEN WILL THE ROCKET BE 300ft? WHAT IS THE MEANING OF THE Y INTERCEPT WHEN WILL IT REACH THE GROUND? I AM UNSURE OF HOW TO START THE PROBLEM. DO I USE THE QUADRATIC FORMULA? 1 solutions Answer 453866 by josmiceli(9819)   on 2013-05-06 11:01:46 (Show Source): You can put this solution on YOUR website! is the height of the rocket from the ground If you want the height to be ft, then Divide through by Use quadratic wquation sec In 2.858 sec the height of the rocket will be 300 ft ------------------ I have to run now- check my math. The method should be OK
 Money_Word_Problems/745328: In 1980 the average price of a home in Brainerd County was \$95,000. By 1987 the average price of a home was \$123,000. Which of the following is a linear model for the price of a home, P in brainerd County in terms of a year, t? let t=0 correspond to 1980. Answers: A) P=123,000-4000t B) P=4000t+95,000 C) P= 123,000- 28,000t D) P= 28,000t + 95,0001 solutions Answer 453803 by josmiceli(9819)   on 2013-05-05 20:11:51 (Show Source): You can put this solution on YOUR website!Use the point slope formula: is plotted on the vertical axis is plotted on the horizontal axis The answer is B)
 Travel_Word_Problems/745124: When Mr. Gomez drives his car to work, the trip takes 30 minutes. When he rides the bus, it takes 45 minutes. If his average driving speed is 12 mph faster than the average speed of the bus, find the distance he travels to work. 1 solutions Answer 453738 by josmiceli(9819)   on 2013-05-05 13:07:44 (Show Source): You can put this solution on YOUR website!Let = the distance to work Let = the speed of the bus Convert minutes to hours By car: (1) By bus: (2) ------------------ Substitute (2) into (1) (1) Multiply both sides by (1) (1) (1) Substitute this result into (2) (2) (2) (2) The distance to work is 18 miles
 Functions/745110: The height s, in feet, of a rock thrown upward at an initial speed of 64 ft/sec from a cliff 50 ft above an ocean beach is given by the function s(t)=-16t^2+64t+50, where t is the time in seconds. Find the maximum height above the beach that the rock will attain.1 solutions Answer 453737 by josmiceli(9819)   on 2013-05-05 12:56:57 (Show Source): You can put this solution on YOUR website!The maximum height of this parabolic curve is when and the equation has the form: In your equation, , so sec -------------- Now find which is the maximum height ft The maximum height is 114 ft Here's the plot:
 Travel_Word_Problems/745117: Megan is going on a long distance road trip. She drives for 14 miles before being able to travel at a constant speed using cruise control. The equation y = 70x + 14 can be used to find her total distance traveled. If y is the total number of miles driven, and x is the number of hours driven after reaching 14 miles, which statement best describes the rate of change in the distance traveled?1 solutions Answer 453736 by josmiceli(9819)   on 2013-05-05 12:45:08 (Show Source): You can put this solution on YOUR website!The rate of change of the distance traveled is the slope of the equation, which is: ( change in y ) / ( change in x ) = 70 mi/hr
 Mixture_Word_Problems/744992: Wilma went to the local market and bought 3 lemons and 5 oranges for \$2.40.The same day and for the same price ,Fran bought 4 lemons and 7 oranges for \$3.31.What was the prices per lemon and the price per orange? Answer is \$o.25 per lemon and \$.33 per orange1 solutions Answer 453642 by josmiceli(9819)   on 2013-05-04 21:46:45 (Show Source): You can put this solution on YOUR website!Let = price of a lemon Let = price of an orange given: (1) ( in cents ) (2) ( in cents ) -------------------- Multiply both sides of (1) by and both sides of (2) by Then subtract (1) from (2) (2) (1) and (1) (1) (1) (1) 25 cents /lemon and 33 cents/orange
 Miscellaneous_Word_Problems/744942: A herd of 575 deer is introduced onto a small. island. At first the herd increases rapidly, but eventually food resources dwindle and the population declines. suppose that the number of deer after t years is given by the following formula N(t)= -t^4 + 2t^2 + 575 please show a step by step on how you got your answer 1 solutions Answer 453639 by josmiceli(9819)   on 2013-05-04 21:36:21 (Show Source): You can put this solution on YOUR website!You didn't finish the question
 Travel_Word_Problems/744989: 1) At 6 a.m., a passenger train and a freight train leave stations that are 360 miles apart and travel toward each other. The passenger train averages twice the speed of the freight train. At 10 a.m., the trains pass each other. Write and solve an equation to find the average speed of each train1 solutions Answer 453638 by josmiceli(9819)   on 2013-05-04 21:27:44 (Show Source): You can put this solution on YOUR website!Think of one train as standing still and the other approaching at the sum of their speeds ( it doesn't matter which train is moving ) -------------------------------------- Let = the speed of the slower train = the speed of the faster train The time the moving train is traveling is 10 AM minus 6 AM = hrs ---------------------------- The average speed of the freight train is 30 mi/hr The average speed of the passenger train is 60 mi/hr --------------- check: freight train: --------------- passenger train: -------------- mi OK
 Mixture_Word_Problems/744940: three solutions contain a certain acid. the first contains 15% acid, the second 35%, and the third 40%. A chemist wishes to use all three solutions to obtain a 75-liter mixture containing 34% acid. If the chemist wants to use twice as much of the 35% solution as of the 40% solution, how many liters, to the nearest 10th, of each solution should be used?1 solutions Answer 453617 by josmiceli(9819)   on 2013-05-04 16:43:03 (Show Source): You can put this solution on YOUR website!Let = liters of 40% solution needed = liters of 35% solution needed Let = liters of 15% solution needed --------------- = liters of acid in 40% solution = liters of acid in 35% solution = liters of acid in 15% solution ---------------- (1) (2) ---------------- (1) and (2) (2) (2) ---------------- Multiply both sides of (1) by and subtract (1) from (2) (2) (1) and, since (1) (1) (1) (1) 21.9 liters of 40% solution are needed 43.8 liters of 35% solution needed 9.2 liters of 15% solution are needed -------------- check: (2) (2) (2) (2) OK
 Mixture_Word_Problems/744895: How much pure water must be mixed with 2 pints of 50% developer to produce a mixture that is 31% developer1 solutions Answer 453616 by josmiceli(9819)   on 2013-05-04 16:20:51 (Show Source): You can put this solution on YOUR website!Let = pints of water needed pint of developer in 50% solution -------------- pints -------------------- check: OK
 logarithm/744927: If log(base 3)2 = x simplify each logarithm a) log(base 3)8 b) log(base 3)24 c) log(base 3)√2 d) log(base 3)6√2 Can you please help me out? Thanks so much in advance:) Can you also show all the steps because it would help me understand :)1 solutions Answer 453615 by josmiceli(9819)   on 2013-05-04 16:12:49 (Show Source): You can put this solution on YOUR website!How well do you understand what logs are? If I say , then is the log is the result So I can rewrite this exactly as: ---------------- The general rules are: ( the base can be 10, or anything else ) ( again, the base can be anything ) ---------------- a) b) c) d)
 Travel_Word_Problems/744932: two airplanes start at the same time and fly toward each other from points 200 km apart at rates of 350 km/h and 400km/h when will they meet1 solutions Answer 453614 by josmiceli(9819)   on 2013-05-04 15:49:57 (Show Source): You can put this solution on YOUR website!Think of one plane as standing still and the other approaching at the sum of their speeds. Equation for the moving plane: hrs min They will meet in 16 min