Aptitude - Problems on Trains - Discussion

As per the given question:
tunnel's length is 3(1/2) i.e. = 7/2
train's length is 1/4.
So as per the formulas we are supposed to add lengths so we add (7/2)+(1/4)

Guys for those who asked doubt here is the answer.

Its given in miles per hour and we have to find time in minutes.

So no need to convert into any other form.

Actually time and distance two different units.we want to find the time of crossing the tunnel. Speed is given in the form of 75 miles/hour so our concern only with hour not distance so change hour to minute and then calculate ur answer.

Total length =7/2 + 1/4 = 15/4 miles
Speed = 75 mile/hour = (75/60)miles/minute

Now time taken is distance / speed = (15/4) / (75/60) = 15*60/4*75 =3 minute.

Time=Distance/velocity ---------------------(1)
time=(15/75*4)=1/20 hrs ---------------------(2)
time=(1/20)*60=3 min ---------------------(3)

I understand all these statement, but i have problem. with the statement (2) that how we just find out the time without converting meter into miles or vice versa. In this they simply find the time without any conversion and it is not so acceptable

Please clear me out..

According to me answer will be c)3.2min

Because the lenth of train has to be taken twice bec. intially train of length 1/4 will enter and then it wil leave the tunnel

Therefore distance travelled=7/2+1/4+1/4=4

Please check it out

Can't we just do it this way

3 1/2 =3.50 and 1/4 = .25

So 3.50+0.25 = 3.75

(3.75/75 as t = dist/speed) t = 3.75/75 = 0.05

Now 0.05 is in hr so 0.05*60 = 3

This method is better then above.

Please can any one clearly explain the formation of expression.

(7/2) + (1/4).

We have given 3(1/2) mile length of the tunnel and train length as 1/4 mile.
So we relate tunnel length and train length

We have to see in 3 1/2 how many 1/4's are there or how many 1/4's make a 3 1/2
3 1/2 is a mixed fraction to make into a proper fration we do as follows
first multiply 2*3=6
next add the numerator 1 to previous results
6+1=7

We have numerator as '7'and keep the denominator '2' as it is
now the proper fraction for 3 1/2 is 7/2

So here total length 7/2+1/4=15/4miles
time taken=distance/speed
time taken=(15/4miles)/75miles/hr
15/4*75=15/300=>1/20hrs
to convert into min v multiply by 60 .
because 1 hr = 60 min
1/20 *60=3mins
here ends the problem

No need of convert miles to kms because it makes the problem complex and even though all units are in miles they get cancelled.

mph--->meters/hour
Mph---->miles/our

Answer is 3 min because.

Given is speed = 75 miles per hour
Total distance is 7/2 + 1/4 = 15/4

Distance is 15/4 because in question it is mentioned that calculate time from entry of tunnel to the point when train's rear left the tunnel.

                        7/2 miles              1/4 miles
           <---------------------------------><------->
            _________________________________   train
 entry of  [               tunnel            ]__________
  tunnel   [_________________________________]__________]--> -->

Hope so this will help.