Towns X is 3600 km to the west of Town Y. An Airline operates non-stop

Question

Towns X is 3600 km to the west of Town Y. An Airline operates non-stop flights between X and Y. Its schedule is tabulated as below. The given time is the local time on the same day.

Departure from Town Y at 4.00PM and Arrival at Town X at 7.30 PM
Departure from Town X at 3.00AM and Arrival at Town Y at 1.30 PM

The planes cruise at the same speed in both directions. However, a steady wind blows from Y to X at 75 KMPH. The effective speed of each plane is affected by this.

Find the time difference between X and Y.

A 1.5 hrs
B. 2 hrs
C. 2.5 hrs
D. 3 hrs
E. 4.5 hrs

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ankitpal10 · Answer

This situation is similar to a boat going upstream and downstream. We have the total distance, speed of the wind and the total time taken for the entire journey.

Since the total time taken to travel between X & Y is 10.5+3.5 = 14 hrs

We can set up the equation as:

3600/(s+75) + 3600/(s-75) = 14

since the terms on the left add up to 14, we need to go the algebraic route as it might be complex/lengthy. As we know that both terms on the LHS add up to 14 we can split it up as 3 and 11 OR 4 and 10 OR 5 and 9 OR 6 and 8. Since 6 and 8 fulfill the equation, I can deduce that s must be 525.

So the time difference must be 2.5 hrs

jasminelin · Answer

what equation does 6 and 8 fulfill that the other combinations dont?
PLEASE HELPPP

lucasd14 · Answer

Bunuel ,  ScottTargetTestPrep ,  IanStewart , could you please share the solution? Thanks!

IanStewart · Answer

It honestly took me a couple of minutes just to understand what the question was asking (maybe it's just me, but I was thinking it was asking the time of a flight from X to Y, and not for the time zone difference). Regardless, you won't see a similar question on the GMAT.

Here, if the planes all go s miles per hour, then because of the wind, going from Y to X the plane will go s+75 mph, and from X to Y it will go s-75 mph.

If there were no time zone difference, then flying from Y to X would take 3.5 hours. But the time changes (the times given are the local times) so it takes 3.5 + t hours, where t is the time difference. Similarly, it takes 10.5 - t hours going the other way.

We know also that the total distance is 3600 miles. Since distance = speed*time, for the trip from Y to X, we get this equation:

3600 = (s + 75)(3.5 + t)

and for the trip from X to Y we get this equation:

3600 = (s - 75)(10.5 - t)

Now this algebra doesn't look fun at all, so I'd be looking for a way to avoid it. We know that t is equal to one of the five answer choices, and questions like this are a rare type where backsolving is actually better than solving directly. We can often eliminate some answers quickly; for example, if you imagine plugging in t = 2 into the first equation, we'll get (s + 75)(5.5) on the right side. That would need to multiply to 3600, but 3600 isn't cleanly divisible by 5.5 (it's like dividing 7200 by 11), so there's almost no chance that answer can be right. The numbers will need to divide neatly. Answer D won't work for the same reason, but A, C and E are candidates. If you test answer A, from the first equation you get 3600 = (s + 75)(5), so s + 75 = 720, and s = 645. Then s - 75 = 570, which isn't going to work in the second equation. If you test C, the first equation becomes (s + 75)(6) = 3600, and s + 75 = 600, so s = 525. Checking if that works in the second equation, we get (s - 75)(10.5 - t) = (525 - 75)(10.5 - 2.5) = 450*8 = 3600, which is exactly what we wanted, so C is the right answer.

The solution ankitpal posted above neatly condenses the algebra into a single equation, with one unknown, and I think it's a better solution than what I just wrote above, from a mathematical viewpoint. But for the GMAT, because we're asked to find the time zone difference t, we can only take advantage of the fact that one answer choice must be the right answer if we preserve t in our equations, so that's why I've done that. But if you want to read a more elegant approach to the question, see that solution.

The "OA" is wrong, incidentally (I imagine it will be edited, but right now it says B is the right answer, and the answer is C). And I just realized I wrote "miles" everywhere when the question uses kilometers, but that doesn't affect any of the math, so I won't bother to fix that.

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Towns X is 3600 km to the west of Town Y. An Airline operates non-stop

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Towns X is 3600 km to the west of Town Y. An Airline operates non-stop

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