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Cities A and B are in different time zones. A is located 3000 km east

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Bunuel
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Cities A and B are in different time zones. A is located 3000 km east [#permalink] New post  08 Jan 2020, 01:50
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Cities A and B are in different time zones. A is located 3000 km east of B. The table below describes the schedule of an airline operating non-stop flights between A and B. All the times indicated are local and on the same day.

Assume that planes cruise at the same speed in both directions. However, the effective speed is influenced by a steady wind blowing from east to west at 50 km per hour.

What is the plane’s cruising speed in km per hour?

(A) 500
(B) 550
(C) 600
(D) 700
(E) Cannot be determined


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BhishmaNaidu99
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Re: Cities A and B are in different time zones. A is located 3000 km east [#permalink] New post  09 Jan 2020, 03:44
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given the data ,

let speed of plane is S , t is difference in the time zone.

Time taken while going from B to A = 7hr - t

Time taken while going from A to B = 4hr + t

total time taken during travelling = 7 + 4 = 11

i.e \(\frac{3000}{s-50} + \frac{3000}{s+50} = 11\) , by plugging in the s = 550kmph exactly.
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Bunuel
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Re: Cities A and B are in different time zones. A is located 3000 km east [#permalink] New post  08 Jan 2020, 01:50
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Bunuel wrote:
Cities A and B are in different time zones. A is located 3000 km east of B. The table below describes the schedule of an airline operating non-stop flights between A and B. All the times indicated are local and on the same day.

Assume that planes cruise at the same speed in both directions. However, the effective speed is influenced by a steady wind blowing from east to west at 50 km per hour.

What is the plane’s cruising speed in km per hour?

(A) 500
(B) 550
(C) 600
(D) 700
(E) Cannot be determined


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Cities A and B are in different time zones. A is located 3000 km east [#permalink] New post  09 Jan 2020, 00:14
Let the time taken for the flight from A to B to Tab and the time from B to A be Tba. Let the speed of the plane be S, and the time difference be Td.
Then from the information provided above, the following equations can be formed.
Tab=7-td --------(1)
Tba=4+td--------(2)
Sab = S+50 -----(3)
Sba = S-50 ------(4)

Since the plane would cover the same distance in a trip from A to B and B to A, Average Speed, Sav, =[(S+50)+(S-50)]/2 = 2S/2 = S.
Average time, Tav, = [(4+td)+(7-td)] = 11/2 = 5.5hrs.

Sav = S = Average distance Between A and B / Average Time = 3000/5.5 = 545 approximately 550km/hr

The answer is, therefore B.
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chanyb
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Re: Cities A and B are in different time zones. A is located 3000 km east [#permalink] New post  09 Jan 2020, 05:59
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T1 + T2 = 4 + 7 = 11 hours
\(T1=\frac{D1}{V1}=\frac{3000}{(S+50)}\)
\(T2= \frac{D2}{V2}=\frac{3000}{(S-50)}\)
\(\frac{3000}{(S+50)}+\frac{3000}{(S-50)}=11\)

At this stage you can either solve the equation (not recommended) or plug in the numbers. 550 is a perfect fit:

\(\frac{3000}{(500+50)}+\frac{3000}{(550-50)}=5+6=11\)

Answer is B
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Re: Cities A and B are in different time zones. A is located 3000 km east [#permalink] New post  18 Aug 2022, 04:54
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Ok, So from A to B the plane would need 3000/(550+50)=5 hours right? but the problem says it needs 4 hours. how come?
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udaypratapsingh99
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Re: Cities A and B are in different time zones. A is located 3000 km east [#permalink] New post  18 Oct 2022, 06:49
Foreheadson wrote:
Ok, So from A to B the plane would need 3000/(550+50)=5 hours right? but the problem says it needs 4 hours. how come?


Can you highlight, from which part of the question you inferred that it needs 4 hours?
I guess, the problem doesn't say that it needs 4 hours.
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Re: Cities A and B are in different time zones. A is located 3000 km east [#permalink] New post  18 Oct 2022, 10:33
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After got the 7 hours for BA and 4 hours for AB, we can see that the time zone difference must be 3/2=1.
Adjusting the travel time by 1 hour, we can get the actual flying time for BA and AB are 6 and 5.
Considering the impact of wind speed, we assume the constant flying speed is S, then we can get two equations
(S -50)*6 hours = 3000 for BA trip, the S, the constant speed, is 3300/6=550
(S+50)*5 hours = 3000 for AB trip, the constant is 2700/5= 550, same as above.
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Re: Cities A and B are in different time zones. A is located 3000 km east [#permalink]
18 Oct 2022, 10:33
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