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# An aircraft flew 600 miles to a town at an average speed of 400 miles

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Math Expert
Joined: 02 Sep 2009
Posts: 59730
An aircraft flew 600 miles to a town at an average speed of 400 miles  [#permalink]

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26 Sep 2018, 05:05
00:00

Difficulty:

35% (medium)

Question Stats:

69% (02:01) correct 31% (02:05) wrong based on 73 sessions

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An aircraft flew 600 miles to a town at an average speed of 400 miles per hour with the wind and made the trip back following the same route at an average speed of 500 miles per hour against the wind. Which of the following is aircraft’s approximate average speed, in miles per hour, for the trip?

(A) 420
(B) 444
(C) 450
(D) 467
(E) 483

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Re: An aircraft flew 600 miles to a town at an average speed of 400 miles  [#permalink]

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28 Sep 2018, 12:40
1
Time take in case 1=distance/time $$= 600/400 = 3/2$$
Time taken in case 2 = distance/time $$= 600/500 = 6/5$$
Total time taken for the entire journey $$= 3/2+6/5 = 27/10$$
Total Distance $$= (600+600) = 1200$$

Total speed = total Distance/Total Time $$= 1200 ÷ 27/10 = (1200*10)/27 = 4000/9 = 444.444$$
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Re: An aircraft flew 600 miles to a town at an average speed of 400 miles  [#permalink]

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28 Sep 2018, 13:19
Since the distance is equal for both trips we can use the shortcut formula

Avg speed = (2*v1 * v2)/(v1 + v2)

Since we also have the variable wind which cancels.

(2*500*400)/(400+500) = 400,000/900 = 4,000/9 = 444.444

Another way would be to assume a value for the wind let it be for example w = 100

400+100 = 500 = v1
500-100 = 400 = v2

Dtotal = d1 + d2 = 600 + 600 = 1,200

T1= 600/500 = 6/5
T2 = 600/400 = 6/4

Avg speed = 1,200/(6/5+3/2) = 1,200/(27/10) = 1,200 * 10/27 = 444.444

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Re: An aircraft flew 600 miles to a town at an average speed of 400 miles  [#permalink]

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29 Sep 2018, 07:27
Distance = 600
Speed = 400
Time = 600/400 = 3/2

Distance = 600
Speed = 500
Time = 600/500 =6/5

Avg spd = TD/TT = 1200/27/10 = 120/27 = 44.4

Hence B
Re: An aircraft flew 600 miles to a town at an average speed of 400 miles   [#permalink] 29 Sep 2018, 07:27
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