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href="trains.html"><strong>BACK</strong></a><h2><b>TRAINS</b></h2><br><pre><font size="4"> <strong>Problems:-</strong><br> (1)Find the time taken by a train 180m long,running at 72kmph in <br> crossing an electric pole<br> Solution :: Speed of the train =72*5/18m/s =20 m/s<br> Distance move din passing the pole = 180m<br> Requiredtime = 180/20 = 9 seconds<br>(2)A train 140 m long running at 60kmph.In how much time will it<br> pass a platform 260m long.<br> Solution ::<br> Distance travelled =140 + 260 m =400 m,<br> speed = 60 * 5/18 = 50//3 m<br> time=400*3 / 50 = 24 Seconds<br>(3)A man is standing on a railway bridge which is 180 m.He finds <br>that a train crosses the bridge in 20 seconds but himself in 8 sec.<br>Find the length of the train and its sppeed<br> Solution ::<br> i)D=180+x<br> T = 20 seconds<br> S= 180+x / 20 ------------ 1<br> ii)D=x<br> T=8 seconds<br> D=ST<br> x=8S ------------- 2<br> Substitute 2 in 1<br> S=180 + 8 S / 20<br> S=15 m/s<br> Length of the train,x is 8 *15 = 120 m<br>(4)A train 150m long is running with a speed of 68 mphIn wht time<br> will it pass a man who is running at a speed of 8kmph in the same<br> direction in which the train is going<br> Solution ::<br> Relative Speed = 68-8=60kmph*5/18 = 50/3 m/s<br> time= 150 * 3 /50 =9sec<br>(5)A train 220m long is running with a speed of 59 k mph /..In what<br> time will it pass a man who is running at 7 kmph in the direction <br> opposite to that in which train is going.<br> Solution ::<br> Relative Speed = 59+7=66kmph*5/18 = 55/3 m/s<br> time= 220/55 * 3 =12sec<br>(6)Two trains 137m and 163m in length are running towards each other on <br> parallel lines,one at the rate of 42kmph & another at 48 mph.In wht time<br> will they be clear of each other from the moment they meet.<br> Solution ::<br> Relative speed =42+48 = 90 *5/18 = 25m/s<br>time taken by the train to pass each other = time taken to cover<br> (137+163)m at 25 m/s<br> = 300 /25 s =12 s<br>(7)A train running at 54 kmph takes 20 sec to pass a platform .Next it <br> takes 12 sec to pass a man walking at 6kmph in the same direction in which<br> the train is going.Find length of the train and length of platform<br> Solution ::<br> Relative speed w.r.t man = 54-6=48kmph<br> the length of the train is 48 * 5/18 * 12 =160m<br> time taken to pass platform =20 sec <br> Speed of the train = 54 * 5/18 =15m/s<br> 160+x =20 *15<br> x=140m<br> length of the platform is 140m<br>(8)A man sitting in a train which is travelling at 50mph observes that a <br> goods train travelling in opposite irection takes 9 sec to pass him .If<br> the goos train is 150m long fin its speed<br> Solution ::<br> Relative speed =150/9 m/s =60 mph<br> speed of the train = 60-50 =10kmph<br>(9)Two trains are moving in the sam e direction at 65kmph and 45kmph.the<br> faster train crosses a man in slower train in18sec.the length of the<br> faster train is<br> Solution ::<br> Relative speed =65-45 kmph = 50/9 m/s<br> Distancce covered in18 s =50/9 * 18 = 100m<br> the length of the train is 100m<br>(10)Atrain overtakes two persons who are walking in the same direction in <br> which the train is going at the rate of 2kmph an 4kmph and passes them <br> completely in 9 sec an 10 sec respectively.the length of train is<br> Solution ::<br> 2kmph = 5/9 m/s<br> 4 mph =10/9 m/s<br> Let the length of the trainbe x meters and its speed is y m/s<br> then x / (y- 5/9) = 9 and x / (y- 10/9) = 10<br> 9y-5 =x and 10(9y-10)=9x <br> 9y-x=5 and 90y-9x=100<br> on solving we get x=50,lenght of trains<br>(11) Two stations A & B are 110 km apart on a straight line.One train starts <br> from A at 7am and travels towards B at 20kmph.Another train starts <br> from B at 8am an travels toward A at a speed of 25kmph.At what time will they meet<br> Solution ::<br> Suppose the train meet x hr after 7am<br> Distance covered by A in x hr=20x km<br> 20x+25(x-1) = 110 <br> 45x=135<br> x=3<br> So they meet at 10 am<br>(12)A traintravelling at 48kmph completely crosses another train having half its length an travelling inopposite direction at 42kmph in12 sec.It also passes a railway platform in 45sec.the length of platform is Solution :: Let the length of the first train be x mt then,the length of second train is x/2 mt relative speed = 48+42 kmph =90 * 5/18 m/s = 25m/s (x+ x/2)/25 =12 x=200 Length of the train is 200m Let the length of the platform be y mt speed f the first train = 48*5/18 m/s = 40/3 m/s 200+y * 3/40 = 45 y=400m(13)The length of a running trsain in 30% more than the length of anpther train B runnng in the opposite direction.To find out the speed of trtain B,which of the following information given in the statements P & Q is sufficient P : The speed of train A is 80 kmph Q : They too 90 sec to cross each other(a) Either P & Q is sufficient(b)Both P & Q are not sufficient(c)only Q is sufficient(d)Both P & Q are neeed Ans: B Solution :: Let the length of th e train A be x mt Length of the train B = 130/100 x mt =13x/10 mt Let the speed of B be y mph,speed of the train A=80mph relative speed= y+80 * 5/18 m/s time taken by the trains t cross each other is gven by 90 = (x + 13x/10)/ (5y+400 / 18) to find y,clearly xis also needed so,both P & Q are not sufficient(14)The speed of a train A,100m long is 40% more than then the speedd of another train B,180m long running in opposite direction.To fin out the speed of B,which of the information given in statements P & Q is sufficient P :The two trains crossed each other in 6 seconds Q : The difference between the spee of the trains is 26kmph(a)Only P is sufficient(b)Only Q is sufficient(c)Both P & Q are needed(d)Both P & Q are not sufficient Ans : A Solution ::Let speed of B be x kmphthen,speed of A =140x/100 kmph =7x/5 mphrelative speed = x + 7x/5 =2x/3 m/stime taken to cross each other = (100+180)*3/2x s =420/x snow,420/x = 6 x=70 mphthus,only P is sufficient(15)The train running at certain speed crosses astationary enginein 20 seconds.to find out the sped of the train,which of the following information is necessary(a)Only the length of the train(b)only the length of the engine(c)Either the length of the train or length of engine(d)Both the length of the train or length of engine Ans : D Solution ::Since the sum of lengths of the tran and the engine is needed, so both the length must be known<a href="trains.html"><strong>BACK</strong></a></font></pre></TD></TR></table></html>?? 快捷鍵說明
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