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James started from his home and drove eastwards at a constant speed. Exactly 90 minutes after James stated from his home, his brother Patrick started from the same point and drove in the same direction as James did at a different constant speed. Patrick overtook James exactly 90 minutes after Patrick started his journey and then continued driving at the same speed for another 2 hours. By what percentage should Patrick reduce his speed so that James could catch up with Patrick in exactly 8 hours after Patrick overtook James?
- a)25%
- b)33%
- c)50%
- d)67%
- e)75%
Correct answer is option 'D'. Can you explain this answer?
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James started from his home and drove eastwards at a constant speed. E...
Given information:
- James drove eastwards at a constant speed.
- Patrick started from the same point 90 minutes later and drove in the same direction as James did at a different constant speed.
- Patrick overtook James after 90 minutes and continued driving at the same speed for another 2 hours.
- We need to find the percentage by which Patrick should reduce his speed so that James could catch up with Patrick in exactly 8 hours after Patrick overtook James.
Calculating the distance covered by James and Patrick:
Let's assume that James' speed is x and Patrick's speed is y.
Distance covered by James in 90 minutes = x * 1.5 = 1.5x
When Patrick overtakes James, the distance covered by Patrick = distance covered by James + 90 minutes of driving time.
So, distance covered by Patrick = x * 1.5 + y * 1.5 = 1.5(x + y)
Distance covered by Patrick in the next 2 hours = 2y
Calculating the time taken by James to catch up with Patrick:
Let's assume that James catches up with Patrick after t hours.
Distance covered by James in t hours = x * t
Distance covered by Patrick in t hours = 1.5(x + y) + 2y = 1.5x + 3.5y
As both of them cover the same distance when James catches up with Patrick, we can equate the above two equations:
x * t = 1.5x + 3.5y
t = 1.5 + 3.5y/x
Calculating the percentage reduction in Patrick's speed:
As per the question, we need to find the percentage by which Patrick should reduce his speed so that James could catch up with Patrick in exactly 8 hours after Patrick overtook James.
So, t = 8 - 1.5 - 2 = 4.5
From the above equation, we can say that t is inversely proportional to x/y.
So, if Patrick reduces his speed by a factor of k, then y = (1/k) * y
Now, t = 1.5 + 3.5y/x becomes t = 1.5 + 3.5[k * (y/x)]
Simplifying, we get t = 1.5 + 3.5/k
So, 4.5 = 1.5 + 3.5/k
k = 3.5/3
k = 1.167
Percentage reduction in Patrick's speed = (1 - 1.167) * 100 = 67%
Therefore, the correct answer is option D - 67%.
- James drove eastwards at a constant speed.
- Patrick started from the same point 90 minutes later and drove in the same direction as James did at a different constant speed.
- Patrick overtook James after 90 minutes and continued driving at the same speed for another 2 hours.
- We need to find the percentage by which Patrick should reduce his speed so that James could catch up with Patrick in exactly 8 hours after Patrick overtook James.
Calculating the distance covered by James and Patrick:
Let's assume that James' speed is x and Patrick's speed is y.
Distance covered by James in 90 minutes = x * 1.5 = 1.5x
When Patrick overtakes James, the distance covered by Patrick = distance covered by James + 90 minutes of driving time.
So, distance covered by Patrick = x * 1.5 + y * 1.5 = 1.5(x + y)
Distance covered by Patrick in the next 2 hours = 2y
Calculating the time taken by James to catch up with Patrick:
Let's assume that James catches up with Patrick after t hours.
Distance covered by James in t hours = x * t
Distance covered by Patrick in t hours = 1.5(x + y) + 2y = 1.5x + 3.5y
As both of them cover the same distance when James catches up with Patrick, we can equate the above two equations:
x * t = 1.5x + 3.5y
t = 1.5 + 3.5y/x
Calculating the percentage reduction in Patrick's speed:
As per the question, we need to find the percentage by which Patrick should reduce his speed so that James could catch up with Patrick in exactly 8 hours after Patrick overtook James.
So, t = 8 - 1.5 - 2 = 4.5
From the above equation, we can say that t is inversely proportional to x/y.
So, if Patrick reduces his speed by a factor of k, then y = (1/k) * y
Now, t = 1.5 + 3.5y/x becomes t = 1.5 + 3.5[k * (y/x)]
Simplifying, we get t = 1.5 + 3.5/k
So, 4.5 = 1.5 + 3.5/k
k = 3.5/3
k = 1.167
Percentage reduction in Patrick's speed = (1 - 1.167) * 100 = 67%
Therefore, the correct answer is option D - 67%.
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James started from his home and drove eastwards at a constant speed. Exactly 90 minutes after James stated from his home, his brother Patrick started from the same point and drove in the same direction as James did at a different constant speed. Patrick overtook James exactly 90 minutes after Patrick started his journey and then continued driving at the same speed for another 2 hours. By what percentage should Patrick reduce his speed so that James could catch up with Patrick in exactly 8 hours after Patrick overtook James?a)25%b)33%c)50%d)67%e)75%Correct answer is option 'D'. Can you explain this answer?
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James started from his home and drove eastwards at a constant speed. Exactly 90 minutes after James stated from his home, his brother Patrick started from the same point and drove in the same direction as James did at a different constant speed. Patrick overtook James exactly 90 minutes after Patrick started his journey and then continued driving at the same speed for another 2 hours. By what percentage should Patrick reduce his speed so that James could catch up with Patrick in exactly 8 hours after Patrick overtook James?a)25%b)33%c)50%d)67%e)75%Correct answer is option 'D'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about James started from his home and drove eastwards at a constant speed. Exactly 90 minutes after James stated from his home, his brother Patrick started from the same point and drove in the same direction as James did at a different constant speed. Patrick overtook James exactly 90 minutes after Patrick started his journey and then continued driving at the same speed for another 2 hours. By what percentage should Patrick reduce his speed so that James could catch up with Patrick in exactly 8 hours after Patrick overtook James?a)25%b)33%c)50%d)67%e)75%Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for James started from his home and drove eastwards at a constant speed. Exactly 90 minutes after James stated from his home, his brother Patrick started from the same point and drove in the same direction as James did at a different constant speed. Patrick overtook James exactly 90 minutes after Patrick started his journey and then continued driving at the same speed for another 2 hours. By what percentage should Patrick reduce his speed so that James could catch up with Patrick in exactly 8 hours after Patrick overtook James?a)25%b)33%c)50%d)67%e)75%Correct answer is option 'D'. Can you explain this answer?.
James started from his home and drove eastwards at a constant speed. Exactly 90 minutes after James stated from his home, his brother Patrick started from the same point and drove in the same direction as James did at a different constant speed. Patrick overtook James exactly 90 minutes after Patrick started his journey and then continued driving at the same speed for another 2 hours. By what percentage should Patrick reduce his speed so that James could catch up with Patrick in exactly 8 hours after Patrick overtook James?a)25%b)33%c)50%d)67%e)75%Correct answer is option 'D'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about James started from his home and drove eastwards at a constant speed. Exactly 90 minutes after James stated from his home, his brother Patrick started from the same point and drove in the same direction as James did at a different constant speed. Patrick overtook James exactly 90 minutes after Patrick started his journey and then continued driving at the same speed for another 2 hours. By what percentage should Patrick reduce his speed so that James could catch up with Patrick in exactly 8 hours after Patrick overtook James?a)25%b)33%c)50%d)67%e)75%Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for James started from his home and drove eastwards at a constant speed. Exactly 90 minutes after James stated from his home, his brother Patrick started from the same point and drove in the same direction as James did at a different constant speed. Patrick overtook James exactly 90 minutes after Patrick started his journey and then continued driving at the same speed for another 2 hours. By what percentage should Patrick reduce his speed so that James could catch up with Patrick in exactly 8 hours after Patrick overtook James?a)25%b)33%c)50%d)67%e)75%Correct answer is option 'D'. Can you explain this answer?.
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ample number of questions to practice James started from his home and drove eastwards at a constant speed. Exactly 90 minutes after James stated from his home, his brother Patrick started from the same point and drove in the same direction as James did at a different constant speed. Patrick overtook James exactly 90 minutes after Patrick started his journey and then continued driving at the same speed for another 2 hours. By what percentage should Patrick reduce his speed so that James could catch up with Patrick in exactly 8 hours after Patrick overtook James?a)25%b)33%c)50%d)67%e)75%Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice GMAT tests.
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