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A pilot flies an aircraft at a certain speed for a distance of 800 km.
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29 Apr 2021, 10:28
29 Apr 2021, 10:28
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Question Stats:
83% (03:15) correct
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A pilot flies an aircraft at a certain speed for a distance of 800 km. He could have saved 40 min by increasing the average speed of the plane by 40 km/h. The average speed of the aircraft is
A. 160
B. 200
C. 240
D. 300
E. 400
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
A. 160
B. 200
C. 240
D. 300
E. 400
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
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Joined: 10 Apr 2015
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Re: A pilot flies an aircraft at a certain speed for a distance of 800 km.
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29 Apr 2021, 12:49
29 Apr 2021, 12:49
Carcass wrote:
A pilot flies an aircraft at a certain speed for a distance of 800 km. He could have saved 40 min by increasing the average speed of the plane by 40 km/h. The average speed of the aircraft is
A. 160
B. 200
C. 240
D. 300
E. 400
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
A. 160
B. 200
C. 240
D. 300
E. 400
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
Let's start with a "word equation"
Since the travel time is less when the speed is increased, we can write: (travel time at REGULAR speed) = (travel time at INCREASED speed) + 40 minutes
Rewrite as: (travel time at REGULAR speed) = (travel time at INCREASED speed) + 2/3 hours
Let x = the REGULAR speed (in kilometers per hour)
So, x + 40 = the INCREASED speed (in kilometers per hour)
Time = distance/speed
So, after some substitution, our "word equation" becomes: 800/x = 800/(x + 40) + 2/3
ASIDE: At this point, we can either plug each answer choice into the above equation, or we can solve the equation. Let's solve it.
Multiply both sides of the equation by 3 to get: 2400/x = 2400/(x + 40) + 2
Multiply both sides by x to get: 2400 = 2400x/(x + 40) + 2x
Multiply both sides by (x + 40) to get: 2400(x + 40) = 2400x + 2x(x + 40)
Expand: 2400x + 96,000 = 2400x + 2x² + 80x
Rearrange and simplify: 2x² + 80x - 96,000 = 0
Divide both sides by 2 to get: x² + 40x - 48,000 = 0
Factor: (x + 240)(x - 200) = 0
So, x = -240 OR x = 200
Since the speed can't be negative, we can be certain that x = 200
Answer: B
gmatclubot
Re: A pilot flies an aircraft at a certain speed for a distance of 800 km. [#permalink]
29 Apr 2021, 12:49
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