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Two friends A and B leave City P and City Q simultaneously and travel towards Q and P at constant speeds. They meet at a point in between the two cities and then proceed to their respective destinations in 54 minutes and 24 minutes respectively. How long did B take to cover the entire journey between City Q and City P?
- a)1 hour 30 minutes
- b)2 hour 30 minutes
- c)60 minutes
- d)30 minutes
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
Two friends A and B leave City P and City Q simultaneously and travel...
Let's assume the distance between City P and City Q is D.
Meeting Point
When friends A and B meet at a point in between the two cities, let's say they meet at a distance of x from City P. So, the remaining distance between the meeting point and City Q is (D - x).
Travel Time
Friend A takes 54 minutes to reach City Q from the meeting point, and friend B takes 24 minutes to reach City P from the meeting point.
Speed Calculation
Since both friends A and B travel at constant speeds, we can calculate their speeds using the formula:
Speed = Distance / Time
For friend A:
Speed of A = D / (54 minutes)
For friend B:
Speed of B = D / (24 minutes)
Since they meet at a point in between the two cities, they would have traveled the same amount of time. Therefore, we can equate the distances traveled by both friends:
x = (D - x)
Simplifying the equation, we get:
2x = D
Solving for x, we get:
x = D/2
Total Time Calculation
Now, we can calculate the total time taken by friend B to cover the entire journey between City Q and City P.
Time taken by B = Time taken to reach the meeting point + Time taken from the meeting point to City P
= 24 minutes + 24 minutes (since the meeting point is equidistant from both cities)
= 48 minutes
Therefore, friend B takes 48 minutes to cover the entire journey between City Q and City P.
Converting into Hours and Minutes
To convert 48 minutes into hours and minutes, we divide 48 by 60 (since there are 60 minutes in an hour):
48 minutes ÷ 60 = 0.8 hours
Since 0.8 hours is equivalent to 48 minutes, friend B takes 0.8 hours or 48 minutes to cover the entire journey between City Q and City P.
Therefore, the correct answer is option C) 60 minutes.
Meeting Point
When friends A and B meet at a point in between the two cities, let's say they meet at a distance of x from City P. So, the remaining distance between the meeting point and City Q is (D - x).
Travel Time
Friend A takes 54 minutes to reach City Q from the meeting point, and friend B takes 24 minutes to reach City P from the meeting point.
Speed Calculation
Since both friends A and B travel at constant speeds, we can calculate their speeds using the formula:
Speed = Distance / Time
For friend A:
Speed of A = D / (54 minutes)
For friend B:
Speed of B = D / (24 minutes)
Since they meet at a point in between the two cities, they would have traveled the same amount of time. Therefore, we can equate the distances traveled by both friends:
x = (D - x)
Simplifying the equation, we get:
2x = D
Solving for x, we get:
x = D/2
Total Time Calculation
Now, we can calculate the total time taken by friend B to cover the entire journey between City Q and City P.
Time taken by B = Time taken to reach the meeting point + Time taken from the meeting point to City P
= 24 minutes + 24 minutes (since the meeting point is equidistant from both cities)
= 48 minutes
Therefore, friend B takes 48 minutes to cover the entire journey between City Q and City P.
Converting into Hours and Minutes
To convert 48 minutes into hours and minutes, we divide 48 by 60 (since there are 60 minutes in an hour):
48 minutes ÷ 60 = 0.8 hours
Since 0.8 hours is equivalent to 48 minutes, friend B takes 0.8 hours or 48 minutes to cover the entire journey between City Q and City P.
Therefore, the correct answer is option C) 60 minutes.
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Community Answer
Two friends A and B leave City P and City Q simultaneously and travel...
Let us assume Car A travels at a speed of a and Car B travels at a speed of b.
Further, let us assume that they meet after t minutes.
Distance traveled by car A before meeting car B = a × t. Likewise distance traveled by car B before meeting car A = b × t.
Distance traveled by car A after meeting car B = a × 54. Distance traveled by car B after meeting car A = 24 × b.
Distance traveled by car A after crossing car B = distance traveled by car B before crossing car A (and vice versa).
⇒ at = 54b ---------- (1)
and bt = 24a -------- (2)
Multiplying equations 1 and 2
we have ab × t2 = 54 × 24 × ab
⇒ t2 = 54 × 24
⇒ t = 36
So, both cars would have traveled 36 minutes prior to crossing each other. Or, B would have taken 36 + 24 = 60 minutes to travel the whole distance.
Hence, the correct option is (c).
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Two friends A and B leave City P and City Q simultaneously and travel towards Q and P at constant speeds. They meet at a point in between the two cities and then proceed to their respective destinations in 54 minutes and 24 minutes respectively. How long did B take to cover the entire journey between City Q and City P?a)1 hour 30 minutesb)2 hour 30 minutesc)60 minutesd)30 minutesCorrect answer is option 'C'. Can you explain this answer?
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Two friends A and B leave City P and City Q simultaneously and travel towards Q and P at constant speeds. They meet at a point in between the two cities and then proceed to their respective destinations in 54 minutes and 24 minutes respectively. How long did B take to cover the entire journey between City Q and City P?a)1 hour 30 minutesb)2 hour 30 minutesc)60 minutesd)30 minutesCorrect answer is option 'C'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Two friends A and B leave City P and City Q simultaneously and travel towards Q and P at constant speeds. They meet at a point in between the two cities and then proceed to their respective destinations in 54 minutes and 24 minutes respectively. How long did B take to cover the entire journey between City Q and City P?a)1 hour 30 minutesb)2 hour 30 minutesc)60 minutesd)30 minutesCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two friends A and B leave City P and City Q simultaneously and travel towards Q and P at constant speeds. They meet at a point in between the two cities and then proceed to their respective destinations in 54 minutes and 24 minutes respectively. How long did B take to cover the entire journey between City Q and City P?a)1 hour 30 minutesb)2 hour 30 minutesc)60 minutesd)30 minutesCorrect answer is option 'C'. Can you explain this answer?.
Two friends A and B leave City P and City Q simultaneously and travel towards Q and P at constant speeds. They meet at a point in between the two cities and then proceed to their respective destinations in 54 minutes and 24 minutes respectively. How long did B take to cover the entire journey between City Q and City P?a)1 hour 30 minutesb)2 hour 30 minutesc)60 minutesd)30 minutesCorrect answer is option 'C'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Two friends A and B leave City P and City Q simultaneously and travel towards Q and P at constant speeds. They meet at a point in between the two cities and then proceed to their respective destinations in 54 minutes and 24 minutes respectively. How long did B take to cover the entire journey between City Q and City P?a)1 hour 30 minutesb)2 hour 30 minutesc)60 minutesd)30 minutesCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two friends A and B leave City P and City Q simultaneously and travel towards Q and P at constant speeds. They meet at a point in between the two cities and then proceed to their respective destinations in 54 minutes and 24 minutes respectively. How long did B take to cover the entire journey between City Q and City P?a)1 hour 30 minutesb)2 hour 30 minutesc)60 minutesd)30 minutesCorrect answer is option 'C'. Can you explain this answer?.
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