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
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 minutesRewrite as:
(travel time at REGULAR speed) = (travel time at INCREASED speed) + 2/3 hoursLet x = the REGULAR speed (in kilometers per hour)
So, x + 40 = the INCREASED speed (in kilometers per hour)
Time = distance/speedSo, after some substitution, our "word equation" becomes:
800/x = 800/(x + 40) + 2/3ASIDE: 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) + 2Multiply both sides by x to get:
2400 = 2400x/(x + 40) + 2xMultiply 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
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Brent Hanneson – Creator of gmatprepnow.com
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