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Two cars travel from different locations at constant speeds. To meet each other after starting at the same time, they take 1.5 hours if they travel towards each other, but 10.5 hours if they travel in the same direction. If the speed of the slower car is 60 km/hr, then the distance traveled, in km, by the slower car when it meets the other car while traveling towards each other, is
- a)100
- b)90
- c)120
- d)150
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
Two cars travel from different locations at constant speeds. To meet e...
Let's assume the distance traveled by the slower car is D km and the distance traveled by the faster car is F km.
When the cars travel towards each other:
- The relative speed of the cars is the sum of their speeds, which is 60 km/hr + F km/hr.
- The time taken to meet each other is given as 1.5 hours.
- The total distance covered by both cars is D + F km.
From the formula: Speed = Distance/Time, we can write the equation:
(D + F)/(60 + F) = 1.5
When the cars travel in the same direction:
- The relative speed of the cars is the difference in their speeds, which is 60 km/hr - F km/hr (as the slower car is traveling slower than the faster car).
- The time taken to meet each other is given as 10.5 hours.
- The total distance covered by both cars is D + F km.
From the formula: Speed = Distance/Time, we can write the equation:
(D + F)/(60 - F) = 10.5
We have two equations with two variables (D and F). We can solve these equations simultaneously to find the values of D and F.
Solving the first equation:
(D + F)/(60 + F) = 1.5
Multiplying both sides by (60 + F):
D + F = 1.5(60 + F)
D + F = 90 + 1.5F
D = 90 + 1.5F - F
D = 90 + 0.5F ........(1)
Solving the second equation:
(D + F)/(60 - F) = 10.5
Multiplying both sides by (60 - F):
D + F = 10.5(60 - F)
D + F = 630 - 10.5F
D = 630 - 11.5F ........(2)
Now, substitute the value of D from equation (1) into equation (2):
90 + 0.5F = 630 - 11.5F
12F = 540
F = 45
Substitute the value of F into equation (1) to find D:
D = 90 + 0.5(45)
D = 90 + 22.5
D = 112.5
Therefore, the distance traveled by the slower car when it meets the other car while traveling towards each other is 112.5 km.
Since none of the given options match this answer, none of the options provided are correct.
When the cars travel towards each other:
- The relative speed of the cars is the sum of their speeds, which is 60 km/hr + F km/hr.
- The time taken to meet each other is given as 1.5 hours.
- The total distance covered by both cars is D + F km.
From the formula: Speed = Distance/Time, we can write the equation:
(D + F)/(60 + F) = 1.5
When the cars travel in the same direction:
- The relative speed of the cars is the difference in their speeds, which is 60 km/hr - F km/hr (as the slower car is traveling slower than the faster car).
- The time taken to meet each other is given as 10.5 hours.
- The total distance covered by both cars is D + F km.
From the formula: Speed = Distance/Time, we can write the equation:
(D + F)/(60 - F) = 10.5
We have two equations with two variables (D and F). We can solve these equations simultaneously to find the values of D and F.
Solving the first equation:
(D + F)/(60 + F) = 1.5
Multiplying both sides by (60 + F):
D + F = 1.5(60 + F)
D + F = 90 + 1.5F
D = 90 + 1.5F - F
D = 90 + 0.5F ........(1)
Solving the second equation:
(D + F)/(60 - F) = 10.5
Multiplying both sides by (60 - F):
D + F = 10.5(60 - F)
D + F = 630 - 10.5F
D = 630 - 11.5F ........(2)
Now, substitute the value of D from equation (1) into equation (2):
90 + 0.5F = 630 - 11.5F
12F = 540
F = 45
Substitute the value of F into equation (1) to find D:
D = 90 + 0.5(45)
D = 90 + 22.5
D = 112.5
Therefore, the distance traveled by the slower car when it meets the other car while traveling towards each other is 112.5 km.
Since none of the given options match this answer, none of the options provided are correct.
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Community Answer
Two cars travel from different locations at constant speeds. To meet e...
To solve this problem, let's assume the speed of the faster car is 'x' km/hr and the distance traveled by the slower car in 1.5 hours is 'd' km.
When the cars travel towards each other:
- The combined speed of the two cars is the sum of their individual speeds: 60 km/hr + x km/hr = (60 + x) km/hr.
- The time taken to meet is given as 1.5 hours.
1. Meeting when traveling towards each other
Using the formula: Speed = Distance/Time
- For the slower car: 60 km/hr = d/1.5 hours
- Rearranging the equation, we find: d = 60 * 1.5 = 90 km
Therefore, the distance traveled by the slower car when it meets the other car while traveling towards each other is 90 km.
2. Meeting when traveling in the same direction
When the cars travel in the same direction, the relative speed of the faster car with respect to the slower car is the difference in their speeds: x km/hr - 60 km/hr = (x - 60) km/hr.
The time taken to meet is given as 10.5 hours.
Using the formula: Speed = Distance/Time
- For the slower car: 60 km/hr = d/10.5 hours
- Rearranging the equation, we find: d = 60 * 10.5 = 630 km
Therefore, the distance traveled by the slower car when it meets the other car while traveling in the same direction is 630 km.
3. Comparison of distances traveled
We can see that the distance traveled by the slower car when traveling towards each other is less than the distance traveled when traveling in the same direction. Therefore, the distance traveled by the slower car when it meets the other car while traveling towards each other is 90 km (Option B).
When the cars travel towards each other:
- The combined speed of the two cars is the sum of their individual speeds: 60 km/hr + x km/hr = (60 + x) km/hr.
- The time taken to meet is given as 1.5 hours.
1. Meeting when traveling towards each other
Using the formula: Speed = Distance/Time
- For the slower car: 60 km/hr = d/1.5 hours
- Rearranging the equation, we find: d = 60 * 1.5 = 90 km
Therefore, the distance traveled by the slower car when it meets the other car while traveling towards each other is 90 km.
2. Meeting when traveling in the same direction
When the cars travel in the same direction, the relative speed of the faster car with respect to the slower car is the difference in their speeds: x km/hr - 60 km/hr = (x - 60) km/hr.
The time taken to meet is given as 10.5 hours.
Using the formula: Speed = Distance/Time
- For the slower car: 60 km/hr = d/10.5 hours
- Rearranging the equation, we find: d = 60 * 10.5 = 630 km
Therefore, the distance traveled by the slower car when it meets the other car while traveling in the same direction is 630 km.
3. Comparison of distances traveled
We can see that the distance traveled by the slower car when traveling towards each other is less than the distance traveled when traveling in the same direction. Therefore, the distance traveled by the slower car when it meets the other car while traveling towards each other is 90 km (Option B).
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Two cars travel from different locations at constant speeds. To meet each other after starting at the same time, they take 1.5 hours if they travel towards each other, but 10.5 hours if they travel in the same direction. If the speed of the slower car is 60 km/hr, then the distance traveled, in km, by the slower car when it meets the other car while traveling towards eachother, isa)100b)90c)120d)150Correct answer is option 'B'. Can you explain this answer?
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Two cars travel from different locations at constant speeds. To meet each other after starting at the same time, they take 1.5 hours if they travel towards each other, but 10.5 hours if they travel in the same direction. If the speed of the slower car is 60 km/hr, then the distance traveled, in km, by the slower car when it meets the other car while traveling towards eachother, isa)100b)90c)120d)150Correct answer is option 'B'. 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 cars travel from different locations at constant speeds. To meet each other after starting at the same time, they take 1.5 hours if they travel towards each other, but 10.5 hours if they travel in the same direction. If the speed of the slower car is 60 km/hr, then the distance traveled, in km, by the slower car when it meets the other car while traveling towards eachother, isa)100b)90c)120d)150Correct answer is option 'B'. 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 cars travel from different locations at constant speeds. To meet each other after starting at the same time, they take 1.5 hours if they travel towards each other, but 10.5 hours if they travel in the same direction. If the speed of the slower car is 60 km/hr, then the distance traveled, in km, by the slower car when it meets the other car while traveling towards eachother, isa)100b)90c)120d)150Correct answer is option 'B'. Can you explain this answer?.
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