Question: A jet is flying 2400 miles from Hawaii to San Francisco. In still air, it flies at 600 mph. There is 40 mph tailwind in the same direction. Exactly how many hours after takeoff would it becomes neutral for the plane to either go to San Francisco or to return to Hawaii in the case of an emergency?
- 1.25 hours
- 1.5 hours
- 1.75 hours
- 2 hours
- 2.5 hours
Correct Answer: C
Solution and Explanation:
Approach Solution 1:
Given to us in the question that a jet is flying 2400 miles from Hawaii to San Francisco. In still air, it flies at 600 mph. There is a 40 mph tailwind in the same direction. It has asked how many hours it will become neutral for the plane to either go to San San Francisco or to return to Hawaii in the case of an emergency.
This is a question from the topic of relative velocity.
It is given that the speed of a jet in still air is 600mph.
This is the absolute speed of the jet.
It is also given that the 40 mph tailwind is in the same direction as the jet.
Because of the tailwind, the speed of the jet will become = 600 + 40 = 640mph
Speed of jet while returning = 600 - 40 = 560mph
The total distance of the journey is 2400 miles.
Now to find the neutral time, let the jet has travelled x miles to reach the neutral point from Hawaii
Now at this neutral point, time taken to go from Hawaii to San-Francisco and San-Francisco to Hawaii is identical
(2400 - x)/640 = x/560
640x = 560*2400 -560x
640x + 560x = 560*2400
1200x = 560 * 2400
X = 560 * 2400 / 1200 = 1120 miles
Travel time after neutral point = (2400 - 1120)/640 = 2 hours
Total time of travel = 2400/640 = 3.75 hours
Initial travel time from Hawaii = 3.75 - 2 hours = 1.75 hours
Therefore after 1.75 hours after takeoff, it will be faster for the jet to go on to San Francisco rather than return to Hawaii.
Approach Solution 2:
Let us assume that the plane had travelled for t hours from Hawaii to reach the neutral point.
It would have covered 640*t miles. And remaining distance it had to cover is 2400 - 640t miles
If the flight were to proceed it would have taken (2400-640t)/640 hours.
If the jet were to go back it would take 640t / 560 hours.
Solving for t we get,
T = 1.75 hours
Therefore the time for which the jet will initially fly to reach the neutral point will be 1.75 hours.
Approach Solution 3:
The problem statement states that:
Given:
- A jet is flying 2400 miles from Hawaii to San Francisco.
- In still air, it flies at 600 mph.
- There is a 40 mph tailwind in the same direction.
Asked:
- To find out the time it will become neutral for the plane to either go to San San Francisco or to return to Hawaii in the case of an emergency.
Because of the tailwind, the speed of the flight = 600+40 = 640 km/hr.
On the other hand, during return, the speed will be = 600- 40 = 560 km/hr.
Let ‘x’ be the distance travelled by the flight to attain the neutral point from Hawaii.
Hence, as per the question, we get:
x/560 ≥ (2400−x)/640
⇒x ≥ 1120 km.
⇒ minimum distance = 1120 km
Therefore, the time taken to cover 1120 km =1120/560= 2 hr.
Total time of travel taken by the flight = 2400/640 = 3.75 hours
Initial travel time from Hawaii = 3.75 - 2 hours = 1.75 hours
“A jet is flying 2400 miles from Hawaii to San Francisco. In still air, it flies at 600 mph”- is a topic of the GMAT Quantitative reasoning section of the GMAT exam. The GMAT Problem Solving questions test the candidates’ aptitudes in assessing quantitative problems accurately. GMAT Quant practice papers enable the candidates to go through varieties of questions that will enhance their mathematical learning.
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