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# M23-09

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Math Expert
Joined: 02 Sep 2009
Posts: 51233
M23-09  [#permalink]

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16 Sep 2014, 00:18
00:00

Difficulty:

25% (medium)

Question Stats:

79% (02:05) correct 21% (02:26) wrong based on 162 sessions

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A plane flying against the wind covers the 900-kilometer distance between two aerodromes in 2 hours. The same plane flying with the wind covers the same distance in 1 hour and 48 minutes. If the speed of the wind is constant, what is the speed of the wind?

A. 18 kmh
B. 20 kmh
C. 22 kmh
D. 25 kmh
E. 27 kmh

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Math Expert
Joined: 02 Sep 2009
Posts: 51233
Re M23-09  [#permalink]

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16 Sep 2014, 00:18
Official Solution:

A plane flying against the wind covers the 900-kilometer distance between two aerodromes in 2 hours. The same plane flying with the wind covers the same distance in 1 hour and 48 minutes. If the speed of the wind is constant, what is the speed of the wind?

A. 18 kmh
B. 20 kmh
C. 22 kmh
D. 25 kmh
E. 27 kmh

Denote $$P$$ and $$W$$ as the speed of the plane and the wind respectively. We know that $$\frac{900}{P - W} = 2$$ and that $$\frac{900}{P + W} = 1.8$$. From this system $$W = 25$$ and $$P = 475$$.

Answer: D
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Re: M23-09  [#permalink]

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16 Nov 2014, 18:59
1
2
Hi Bunuel, I just wanted to fill in some of the algebra in between the steps you listed. If I you know of a faster way to get through the algebra, I'd love to hear your input.

$$\frac{900}{P - W} = 2$$ and that $$\frac{900}{P + W} = 1.8$$

2(P-W) = 1.8(P+W)

2P - 2W = 1.8P + 1.8W

.2P = 3.8W

2P = 38W

P = 19W

Since it took the plane 2 hours to cover 900 while flying against the wind, we know that the speed of the plane minus the speed of the wind = 450.

P - W = 450

Replace P with 19W

19W - W = 450

18W = 450

W = 25
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Re: M23-09  [#permalink]

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05 Jan 2017, 01:06
since we know both speeds of the plane when it is both with and against the wind, why are we adding 'p' for speed, instead of 500 km/hr and 450 km/hr
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Posts: 51233
Re: M23-09  [#permalink]

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05 Jan 2017, 02:25
npin2 wrote:
since we know both speeds of the plane when it is both with and against the wind, why are we adding 'p' for speed, instead of 500 km/hr and 450 km/hr

It's a relative speed thing. When flying against the wind the actual speed is P - W and when flying with the wind the actual speed is P + W.
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Re: M23-09  [#permalink]

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06 Jan 2017, 09:28
Please help, when bodies move in opposite direction speed is added- P+W - wind and plane are against and bodies in same it should P-W. Please suggest.
Math Expert
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Re: M23-09  [#permalink]

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07 Jan 2017, 02:36
C3BISHT wrote:
Please help, when bodies move in opposite direction speed is added- P+W - wind and plane are against and bodies in same it should P-W. Please suggest.

For relative speed, check:
https://www.veritasprep.com/blog/2012/0 ... elatively/
https://www.veritasprep.com/blog/2012/0 ... -concepts/

Hope it helps.
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Re: M23-09  [#permalink]

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26 Feb 2018, 07:03
Can you make it more clear why 1.8 instead of 1.48? I understand that 80% of 60 (1 hour) is 48 minutes, BUT anyways why cant we just pick 1.48? ))
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Posts: 51233
M23-09  [#permalink]

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26 Feb 2018, 07:13
LevanKhukhunashvili wrote:
Can you make it more clear why 1.8 instead of 1.48? I understand that 80% of 60 (1 hour) is 48 minutes, BUT anyways why cant we just pick 1.48? ))

1 hour and 48 minutes = 1.8 hours, while 1.48 hours is 1 hour 28 minutes 48 seconds.
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Re: M23-09  [#permalink]

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26 Feb 2018, 12:42
1
Bunuel wrote:
LevanKhukhunashvili wrote:
Can you make it more clear why 1.8 instead of 1.48? I understand that 80% of 60 (1 hour) is 48 minutes, BUT anyways why cant we just pick 1.48? ))

1 hour and 48 minutes = 1.48 hours, while 1.8 hours is 1 hour 28 minutes 48 seconds.

Sorry for correcting ,you have shown the conversion incorrectly
1.48 hrs = 1 hour 28 minutes 48 seconds while 1.8 hrs = 1 hour 48 minutes
Math Expert
Joined: 02 Sep 2009
Posts: 51233
Re: M23-09  [#permalink]

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26 Feb 2018, 13:48
rhine29388 wrote:
Bunuel wrote:
LevanKhukhunashvili wrote:
Can you make it more clear why 1.8 instead of 1.48? I understand that 80% of 60 (1 hour) is 48 minutes, BUT anyways why cant we just pick 1.48? ))

1 hour and 48 minutes = 1.48 hours, while 1.8 hours is 1 hour 28 minutes 48 seconds.

Sorry for correcting ,you have shown the conversion incorrectly
1.48 hrs = 1 hour 28 minutes 48 seconds while 1.8 hrs = 1 hour 48 minutes

Edited the typo. Thank you for noticing. +1.
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Re: M23-09 &nbs [#permalink] 26 Feb 2018, 13:48
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# M23-09

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