a train leaves Richmond VA going 300 miles to DC in 5 hours making 2½ stops- whats train speed minus stops?
543890
It takes four hours to travel those 300 miles, not counting the stops, so the average speed is 75mph (300 divided by 4).\n\nWith the wind slowing it down, it would be traveling 65mph.  It would then take 4.615 hours in transit (300 divided by 65), which works out to 4 hours 37 minutes (60 minutes * .615 to get the fraction of an hour, plus the four hours).  Add the two half hour stops back in and the total time including stops is 5 hours 37 minutes.
17281
The answer is 15 to 45 miles per hour
742241
The second problem is easier than the first problem, so I'll tackle it first.\n\nLet's imagine that the trip is 120 miles. The distance doesn't matter if the average rates are as given above.\n\nIt takes 3 hours to travel 120 miles at 40 miles per hour.\nIt takes 2 hours to travel 120 miles at 60 miles per hour.\n\nSo it took 5 hours to travel a total of 240 miles.\n\nThis is an average rate of 48 miles per hour.\n\nI'll work on the first problem and hopefully I'll get back to you.\n\nUPDATE\n\nI think I have the first problem solved as well. It involves an infinite series! Call the people involved A and B.\n\nThe probability that A wins on the first toss is 1/2.\n\nIf A doesn't win on the first toss, then the probability that B wins on the second toss is also 1/2. But this only happens in 1/2 of all games. (In the other half, A won on the first toss.)\n\nIf B doesn't win on the second toss, the the probability that A wins on the third toss is also 1/2. But this only happens in 1/4 of all games (In half the other games, A won on the first toss. In half the remaining games - 1/4 of all games, B won on the second toss.\n\nFollowing this logic, A wins:\n\n1/2 + 1/4(1/2) + 1/16(1/2) + 1/64(1/2) + ...\n\nof all games.\n\nB wins:\n\n1/2(1/2) + 1/8(1/2) + 1/32(1/2) + ...\n\nof all games.\n\nLooking again at A, we have:\n\n1/2(1 + 1/4 + 1/16 + 1/64 + ...)\n\nThe term in parentheses is an infinite series having initial term 1 and ratio 1/4.\n\nThe sum of an infinite series having ratio whose absolute value is less than 1 is equal to:\n\na/(1 - r)\n\nWith a = 1, and r = 1/4, the sum = 4/3. So:\n\n1/2(1 + 1/4 + 1/16 + 1/64 + ...) = 1/2 * 4/3 = 2/3\n\nLooking again at B, we have:\n\n1/2(1/2 + 1/8 + 1/32 + 1/128 + ...)\n\nThis sum should be half of the sum of the infinite series in A.\n\nWith a = 1/2 and r = 1/4, a/(1 -r) = 2/3\n\nSo:\n\n1/2(1/2 + 1/8 + 1/32 + 1/128 + ...) = 1/2 * 2/3 = 1/3.\n\nA should win 2/3 of the time, and B should win 1/3 of the time. There is an advantage to going first!
810178
180 miles per hour to go 400 miles is 2.22 hours or about 2 hours and 18 minutes. Stopping for 2 minutes would make the total time 2 hours and 20 minutes.
782056
150\n\nIf we first ignore that each color be used once, there are 3^5 ways to paint the train.\nThen, subtract 2^5 ways that the train could be painted with only red or blue, subtract 2^5 with only blue or yellow and subtract 2^5 ways with only red and yellow then add 3 back because we subtracted all blue , all red and all yellow twice each.\n=243 - 3*2^5 + 3 \n=243 - 96 + 3\n=150
210963
I assume you mean New York.  Grand Central to Mount Kisco trains leave about every 30 minutes travel time is between 50 and 56 minutes. Go to:\nhttp://as0.mta.info/mnr/schedules/sched_form.cfm\nPut in the time and day you are travelling and it will tell you anything you want to know.
1181326
Tim is right.  i just want to explain it further so you will understand.\n\nso the problem is we are looking for the time spent in both trips. lets call it "X". one is 1 hour longer than the other so we can call it "X + 1". \n\nif trip1 with a distance of 180 miles is taken in X with an additional 1 hour we can call this equation as 180 per X+1 or in mathematical form its 180/(X+1)\n\nif trip 2 with a distance of 135 miles is taken in X we can call it 135 per X or 135/X\n\nwe have now 2 equations 180/X+1 and 135/X\n\nsince the rates are the same we can say that the rate for 180/(X+1) is equal to rate for 135/X.  or in equational form it is\n180/(X+1)=135/X.\n\nWe now have a working equation.  If you notice, we are dealing with fractions and to equate it we need to transpose it using cross multiplication.  Cross multiplication is done by pairing the numerator of one side to the denominator of the other side and then proceed to multiplication.\n\nlooking at the working equation, we will pair 180 and X or 180X and another pair which is 135 and (X+1) or 135(X+1)\n\nnow we have a new working equation 135(X+1) = 180X\n\nto simplify 135(X+1) we multiply 135 with X and with 1. 135 and X is equal to 135X and 135 and 1 is equal to 135\n\nnow we have simplified the equation to 135X + 135 = 180X\n\nto get the value of X, we combine similar terms.  they are 135X and 180X.  We combine this by transposition.  Remember that in order not to change the value of the equation we must change the sign of what is moved to another side.  In this case i will move 180X to pair it with 135X and move 135 to the other side. so now we get 135X - 180X = -135\n\nwe simplify the like terms and we get -45X.\n\nnow we have -45X = -135\n\nbut we are only looking for X so we must eliminate -45 from the X.  identify the numerical coefficient of X which is -45 and devide it from the original. what you do to one side, you should also do it to the other.\n\n-45X/-45 = -135/-45 with this equation we can simplify it into\nX=3\n\nnow we have the value for X\n\nso one trip will be 3 and since another is 1 hour longer then it must 3 + 1 = 4\n\nheres the solution\n\n180/(X+1)    =      135/X\n135(X+1)     =      180X\n135X + 135   =    180X\n135X - 180X   =    -135  \n            -45X   =    -135\n         -45X/-45=    -135/-45\n                   X =  3\n          \n             X + 1 =  trip 2\n             3+1 = 4
557602
This is how you solve it. Use dimmensional canellation, but you will have to do it twice and subtract the difference\n\nA. (5 miles/1)  *   (1 hr/55 mi)  * (60 min/1 hr)\n   =5.45 minutes\n \n   \nB. (5 miles/1)*  (1 hr/65 miles) * (60 min/1 hr)\n   =4.6 minutes\n    \nYou saved 1.2 minutes. Not much at all. Which is what they say, speeding only saved 2 or so minutes in a 15-20 minute trip. BUt it tears the bejesus out of your engine
965437
okay when does the train leave?
1007024
distance equals rate times time\nThat is,\nd = rt\nd = 117 and t = 2.25\nSo we have\n117 = r(2.25) or\nr = 117/2.25\nr = 52 mph
735262
1.  The key here is to understand how far the two trains have traveled in total during the first 3 hours.  We are told that the two trains started 500 miles apart, and 3 hours later are now 80 miles apart.  Thus they traveled 420 miles in total. \n\nIf you let x represent the rate of speed that the Freight train is traveling, and x+20 represent the rate of speed that the Passenger train is traveling, you can set the following algebric equation:\n\n3 hrs * x mi/hr  + 3 hrs * ( 20 + x ) mi/hr = 420\n 3x + 60 + 3x = 420\n6x = 360\nx =60 mi/hr.\nx+20 = 80 mi/hr.\n\n2.  The key is too figure out the total number of employees needed to break even.  Regardless of how many employees you have, we are told that it costs $2000 per day to run the factory.  In addition to that  we are told that for each employee, we must pay him or her $300.  These are the total costs for the operation.\n\nOn the other hand, we are told that each employee can produce $500 in revenue each day.\n\nThus, we need to create an algebric equation where the total costs = the total revenue\n\nLet x represent the number of workers, and set up the following algebric equation:\n\nCosts = Revenue\n\n$2000 (Fixed Costs) + $300 * x (Variable Costs) = $500 * x\n\n2000 + 300x = 500x\n2000 = 200x\n10 = x\n\nYou will need 10 workers to break even, and the total gross value of ball bearings produced will be 10 * $500 or $5000.\n\nHope that I have cleared things up for you!
314862
Charleston to DC is 536 miles - 8.5 hours.\n\nColumbia to DC is 483 miles - 7.5 hours\n\nGreenville to DC is 496 miles - 8.0 hours\n\nFlorence to DC is 407 miles - 6.5 hours
669522
It is easiest to think of this in 2 steps.  First, how long does it take the east bound train going 65 mph to travel the 175 miles to the station?\n\nanswer: 175/65=2.6923 hours\n\nStep 2:  How fast does the westbound train need to go to travel the 63 miles in 2.6923 hours?\n\nanswer 63/2.6923 = 23.4 mph
36001
A: 56 mph x 1.5 hours = 84 miles\n\n\nB: Distance = 100 total miles - 84 miles = 16 miles.\nTime = 30 minutes = 0.5 hours.\n\nAverage speed = 16 miles / 0.5 hours = 32 miles per hour.\n\n\nC: Total trip miles = 100 miles\nTotal time = 2 hours (1 hour 30 minutes for first leg, 30 minutes for final leg)\n\nAverage speed = 100 miles / 2 hours = 50 miles per hour.
350753
wather train?????\ninteresting
685470
the speed = distance/time
741279
Total distance traveled divided by total time in transit.\n\nr = d/t.