A train M leaves City A at 5 am and reaches City B at 9am .Another train N leaves City B at 7am and reaches City A at 1030am At what time do the 2 trains cross one another? Source :Review Prep Book

Time that M takes - 4 hours Time that N takes - 3.5 hours Speed of M - d/4 speed of n - d/3.5 Distance traveled by train M in 2 hours (as N leaves 2 hours after M ) = d/4 * 2 = d/2 That means M has already traveled half the distance by the time N leaves. Hence now to cover d/2 Speed = d/4 + d/3.5 d/2/(d/4 + d/3.5) =14/15 hours or 56 minutes

IMO 7:56 am T1 = 4 hrs T2 = 3.5 hrs train N starts at 7 am by that time train M has traveled d / 2 of the distance Now the remaining distance = d/2 based on the formula d = vt ....the ratio of the times will be reciprocals of d1/d2 t1/t2 = d2/d1 4 / 3.5 = d2/d1 d1/d2 = 7/8 to calculate time lets look at train M distance covered by train M = 7/15 x d /2 = 7d /30 speed of train M = d / 4 time taken by train M = d/v = 7d/30 x 4/d = 14/15 hrs = 15/16 x 60 = 56 minutes Thus the time at which the two trains meet is 7:56 am

though i wonder why you were answering your own question ?

neoreaves wrote:though i wonder why you were answering your own question ? Someone once said, "There is always a better method". For questions I find hard I like to see other methods, and besides since I am posting, it would later be easier to consolidate the questions I found hard. Cheers

i'll use almost the same method as eaakbari has ... except i'll make use of the following equation. time taken by A & B working together = a*b/(a+b) at 7am .. A has traveled half the distance .. so time till destination = 2hrs time required by B to travel half the distance = 3.5/2 = 7/4 time taken by A & B working together = (2*7/4) / (2+7/4) = 14/15 hrs = 56mins so 7:56am

eaakbari wrote:A train M leaves City A at 5 am and reaches City B at 9am .Another train N leaves City B at 7am and reaches City A at 1030am At what time do the 2 trains cross one another? Source :Review Prep Book We can plug in our own value for the distance between City A and City B. Since train M travels the distance in 9-5 = 4 hours and train N travels the distance in 10.5-7 = 3.5 hours, we should plug in a value that is divisible by 4 and 3.5. Let d = 28 miles. Rate for M alone = d/t = 28/4 = 7 miles per hour. Distance traveled by M from 5am to 7 am = r*t = 7*2 = 14 miles. Distance remaining = 28-14 = 14 miles. Rate for N alone = d/t = 28/3.5 = 8 miles per hour. Combined rate for M+N = 7+8 = 15 miles per hour. Time for M+N to travel the remaining distance = d/r = 14/15 hours = 56 minutes. Time when M and N will meet = 7am + 56 minutes = 7:56am.