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A pilot flies an aircraft at a certain speed for a distance of 800 km.
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28 Nov 2020, 06:47
28 Nov 2020, 06:47
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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
A. 160
B. 200
C. 240
D. 300
E. 400
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6804
Given Kudos: 799
Location: Canada
Re: A pilot flies an aircraft at a certain speed for a distance of 800 km.
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28 Nov 2020, 07:34
28 Nov 2020, 07:34
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Top Contributor
WarriorWithin 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
A. 160
B. 200
C. 240
D. 300
E. 400
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
Cheers,
Brent
General Discussion
GMAT Tutor
Joined: 24 Jun 2008
Posts: 4127
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Q51 V47
Re: A pilot flies an aircraft at a certain speed for a distance of 800 km.
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28 Nov 2020, 10:42
28 Nov 2020, 10:42
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Say s is his original speed, and t his original time. We know by increasing the speed by 40, the time drops by 2/3 of an hour (we need to get the same unit of time, so 40 minutes needs to be rewritten as 2/3 hours). When we multiply speed and time in each case, we must get the total distance of 800:
st = 800
(s + 40)(t - 2/3) = 800
The algebra in questions like this (where you know a number like 800 is equal to two different, but related, products) can be very messy. It's almost always fastest to test answer choices, but only if you first eliminate the least plausible candidates. That's easier to do on actual GMAT questions than it is here, because the numbers here aren't really like what you see on the real test. But if you imagine that t is an integer here (which will almost always turn out to be true), then t - 2/3 will be an integer plus one third. Since t - 2/3 = 800/(s + 40), when we plug in various values of 's' from the answer choices, we'll want 800/(s + 40) to cancel down to something with only 3 in the denominator. That clearly won't happen if we plug in 240, 300 or 400, since in those cases, s + 40 is 280, 340 and 440, and we'll get 7, 17 and 11 in our denominator respectively. But if we test answer B, s = 200, first in the equation st = 800, we find t = 4, and then in the second equation:
240(t - 2/3) = 800
t - 2/3 = 800/240 = 10/3
t = 12/3 = 4
we get the same value of t both times, so B is correct.
st = 800
(s + 40)(t - 2/3) = 800
The algebra in questions like this (where you know a number like 800 is equal to two different, but related, products) can be very messy. It's almost always fastest to test answer choices, but only if you first eliminate the least plausible candidates. That's easier to do on actual GMAT questions than it is here, because the numbers here aren't really like what you see on the real test. But if you imagine that t is an integer here (which will almost always turn out to be true), then t - 2/3 will be an integer plus one third. Since t - 2/3 = 800/(s + 40), when we plug in various values of 's' from the answer choices, we'll want 800/(s + 40) to cancel down to something with only 3 in the denominator. That clearly won't happen if we plug in 240, 300 or 400, since in those cases, s + 40 is 280, 340 and 440, and we'll get 7, 17 and 11 in our denominator respectively. But if we test answer B, s = 200, first in the equation st = 800, we find t = 4, and then in the second equation:
240(t - 2/3) = 800
t - 2/3 = 800/240 = 10/3
t = 12/3 = 4
we get the same value of t both times, so B is correct.
