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

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Cities A and B are in different time zones. A is located 3000 km east  [#permalink]

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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.
Image
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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Re: Cities A and B are in different time zones. A is located 3000 km east  [#permalink]

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New post 08 Jan 2020, 01:50
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.
Image
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]

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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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Re: Cities A and B are in different time zones. A is located 3000 km east  [#permalink]

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

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New post 09 Jan 2020, 05:59
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] 09 Jan 2020, 05:59
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