Problem Solving

Hi Aman verma,

Eric and I noticed that you haven't been back to BTG in a while.
And we were wondering why an active user like yourself hasn't been
participating recently. Your contributions to BTG have been a real asset
to the community, and we'd love to see you continuing to be apart of the
site.

Please let me know if there is anything we can do to help you or if you
would like to talk about anything else.


dp



David Park | CEO | Beat The GMAT

I thank David and Eric for remembring me and considering me worthwhile for this site. Now I really need to improve my score from 610 to 720+ and I will be requiring a lot of help in the form of guidance and advice from all of you in this regard. But as a token of comeback I post this elementary problem for my fellow friends from whom also I will be requiring guidance to raise my score :

Q: Amtrack Train leaves Connecticut at 6 am and two hours later another train New York Express leaves Connecticut. Both trains arrive New York at 4 pm on the same day. If the difference between their speed be 10 km/ph, what is the average speed of both the trains over entire route :

a)40.22 km/ph

b)41.33 km/ph

c)42.66 km/ph

d)44.44 km/ph

e)46.55 km/ph

Aman welcome back to the forums...

difference is speeds is 10
say the distance is X

then
(X/8)-(X/10)=10
solve the equation=>X=400
now
total distance/total time = average speed
(400+400)/(10+8)
=400/9
=44.44 (trick here is 1/9 is 0.111*)

My approach is this:

Lets assume

Train 1 - Leaves @ 6 AM whose speed is S1 and time taken is T1
Train 2 - Leaves @ 8 AM whose speed in S2 and time taken in T2
Distance - D between Connecticut and New York


Step 1:

Make an equation.

The speeds of the two trains are:

S1 = D/T1 => S1*T1=D -- 1st Equation

S2 = D/T2 => S2*T2=D -- 2nd Equation

Since both the trains travel the same distance lets equate Equation 1 and Equation 2

S1*T1=S2*T2


Step 2:

Train 1 takes 10 hours to reach NY => T1=10
Train 2 takes 8 hours to reach NY => T2=8

Let the speed S1 of the train1 be x.
So the speed S2 of the train2 will be x+10 (As per the info provided in the question)

x*10=(x+10)*8

=>10x=8x+80
=> 2x=80
=> x=40

So,
S1=x=40 kmph and
S2=x+10=50 kmph


Step 3:

Now we need to calculate the average speeds of both the trains.
(Though this question looks like Time, Speed Distance question at the first glance, it is actually a weighted average question)

Train 1 travels @ 40 kmph for 10 hours => 400 kms
Train 2 travels @ 50 kmph for 8 hours => 400 kms

Train 1 and Train 2 together take 18 hours to travel 800 kms

So, the average speed of both the trains is

(400+400)/18 = 44.44 kmph