Two trains, 100 miles apart, travelling towards each other on parallel

Question

Two trains, 100 miles apart, travelling towards each other on parallel tracks pass each other at x hours. If the same two trains were to travel in the same direction, starting 100 miles apart, they would meet each other at y hours. What is the ratio of the speed of the faster train to that of the slower train?

A. \(\frac{y}{x}\)
B. \(\frac{2y}{x+y}\)
C. \(\frac{y + x}{y -x}\)
D. \(\frac{y}{y-x}\)
E. \(\frac{y+x}{x}\)

A.  \frac{y}{x}

B.  \frac{2y}{x+y}

C.  \frac{y + x}{y -x}

D.  \frac{y}{y-x}

E.  \frac{y+x}{x}

boyagao · Accepted Answer

Let's call the faster train A and the slower train B.

In the first scenario, A and B travel a total of 100 miles in X hours. This gives us the following equation: 
AX + BX = 100

In the second scenario, B is ahead of A by 100 miles but they eventually meet at some point after Y hours. This gives us the following equation:
AY = 100 + BY

The question asks for the following equation: 
A/B = ?

We can arrange the second equation to equal the first:
AY - BY = 100 = AX + BX

Now, we can move the As to one side and the Bs to the other and factor them out on either sides:
AY - AX = BX + BY
A(Y - X) = B(X + Y)

Now simply arrange to get A/B on one side:
A(Y - X)/B = (X + Y)
A/B = (X + Y)/(Y - X)

Therefore the answer is (X + Y)/(Y - X), which is equivalent to (Y + X)/(Y - X)

KarishmaB · Answer

Take smart numbers: Say x = 2 hrs and y = 5 hrs

So when covering the distance together, sum of speeds = 100/2 = 50 mph = s1 + s2

When travelling in same direction, difference of speeds = 100/5 = 20 mph = s1 - s2

Then s1 = 35 and s2 = 15

s1/s2 = 35/15 = 7/3

Only (C) satisfies

Vigasimrair · Answer

The question may be solved also by the use of real numbers instead of X and Y.

Let A have a speed 66 and B - 33.
So they will cover 100 km in 1 hour.
And A will overtake B in 3 hours (if there will be 100 km between them).

So all we need is to find the appropriate proportion which will give us 66/33=2/1

Only C is ok: 
(Y+x)/(y-x) = (3+1)/(3-1) =4/2=2/1

Posted from my mobile device

Harsh2111s · Answer

By using concept of relative velocity this question can be solved in real quick time.

Case 1: Trains travelling in opposite direction.
Let speed of trains are S1 and S2.
Hence given time to cross each other =x=100/(S1+S2)

Case 2 : Trains travelling in same direction.

Here time for one train to cross the other=y=100/(S1-S2)

Solving above equation we get
S1/S2=y+x/y-x

adewale223 · Answer

Let the faster speed be a and the slower speed be b.

First statement

x = 100/a+b

ax + bx = 100

Second statement

y = 100/a-b

ay - by = 100

Therefore

ax + bx = ay-by

ax - ay = -by -bx

a(x-y) = b(-y -x )

a/b = -y-x/x- y

Multiplying both numerator and denominator gives

y + x/y-x.

Answer is C.

Posted from my mobile device

saynchalk · Answer

Please explain the S1/S2  part a little more

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

Two trains, 100 miles apart, travelling towards each other on parallel

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

GMAT Problem Solving (PS) Questions

Two trains, 100 miles apart, travelling towards each other on parallel

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia