Problem Solving

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.