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Places A and B are 100 km apart on a highway. One car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds, they meet in 5 hours. If they travel towards each other, they meet in 1 hour. What are the speeds of the two cars?
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Places A and B are 100 km apart on a highway. One car starts from A an...
Let the speed of 1st car and 2nd car be u km/h and v km/h.Respective speed of both cars while they are travelling in same direction = (u - v) km/hRespective speed of both cars while they are travelling in opposite directions i.e., travelling towards each other = (u v) km/hAccording to the question,5(u - v) = 100⇒ u - v = 20 ... (i)1(u v) = 100 ... (ii)Adding both the equations, we get2u = 120u = 60 km/h ... (iii)Putting this value in equation (ii), we obtainv = 40 km/hHence, speed of one car = 60 km/h and speed of other car = 40 km/h
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Places A and B are 100 km apart on a highway. One car starts from A an...
Given Information:
- Distance between places A and B: 100 km
- Time taken to meet when traveling in the same direction: 5 hours
- Time taken to meet when traveling towards each other: 1 hour
Let's assume:
- Speed of the car starting from A: x km/h
- Speed of the car starting from B: y km/h
When traveling in the same direction:
- Relative speed = x - y
- Time taken to meet = 5 hours
- Distance traveled = 100 km
Using the formula: Distance = Speed x Time
100 = (x - y) x 5
100 = 5x - 5y
20 = x - y (Equation 1)
When traveling towards each other:
- Relative speed = x + y
- Time taken to meet = 1 hour
- Distance traveled = 100 km
Using the formula: Distance = Speed x Time
100 = (x + y) x 1
100 = x + y (Equation 2)
Now, we have two equations:
1) 20 = x - y
2) 100 = x + y
Solving these equations simultaneously:
Adding Equation 1 and Equation 2:
20 + 100 = 2x
120 = 2x
x = 60 km/h
Substitute x back into Equation 2:
100 = 60 + y
y = 40 km/h
Therefore, the speeds of the two cars are:
- The car starting from A: 60 km/h
- The car starting from B: 40 km/h
- Distance between places A and B: 100 km
- Time taken to meet when traveling in the same direction: 5 hours
- Time taken to meet when traveling towards each other: 1 hour
Let's assume:
- Speed of the car starting from A: x km/h
- Speed of the car starting from B: y km/h
When traveling in the same direction:
- Relative speed = x - y
- Time taken to meet = 5 hours
- Distance traveled = 100 km
Using the formula: Distance = Speed x Time
100 = (x - y) x 5
100 = 5x - 5y
20 = x - y (Equation 1)
When traveling towards each other:
- Relative speed = x + y
- Time taken to meet = 1 hour
- Distance traveled = 100 km
Using the formula: Distance = Speed x Time
100 = (x + y) x 1
100 = x + y (Equation 2)
Now, we have two equations:
1) 20 = x - y
2) 100 = x + y
Solving these equations simultaneously:
Adding Equation 1 and Equation 2:
20 + 100 = 2x
120 = 2x
x = 60 km/h
Substitute x back into Equation 2:
100 = 60 + y
y = 40 km/h
Therefore, the speeds of the two cars are:
- The car starting from A: 60 km/h
- The car starting from B: 40 km/h
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Places A and B are 100 km apart on a highway. One car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds, they meet in 5 hours. If they travel towards each other, they meet in 1 hour. What are the speeds of the two cars?
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Places A and B are 100 km apart on a highway. One car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds, they meet in 5 hours. If they travel towards each other, they meet in 1 hour. What are the speeds of the two cars? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Places A and B are 100 km apart on a highway. One car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds, they meet in 5 hours. If they travel towards each other, they meet in 1 hour. What are the speeds of the two cars? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Places A and B are 100 km apart on a highway. One car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds, they meet in 5 hours. If they travel towards each other, they meet in 1 hour. What are the speeds of the two cars?.
Places A and B are 100 km apart on a highway. One car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds, they meet in 5 hours. If they travel towards each other, they meet in 1 hour. What are the speeds of the two cars? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Places A and B are 100 km apart on a highway. One car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds, they meet in 5 hours. If they travel towards each other, they meet in 1 hour. What are the speeds of the two cars? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Places A and B are 100 km apart on a highway. One car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds, they meet in 5 hours. If they travel towards each other, they meet in 1 hour. What are the speeds of the two cars?.
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Places A and B are 100 km apart on a highway. One car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds, they meet in 5 hours. If they travel towards each other, they meet in 1 hour. What are the speeds of the two cars?, a detailed solution for Places A and B are 100 km apart on a highway. One car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds, they meet in 5 hours. If they travel towards each other, they meet in 1 hour. What are the speeds of the two cars? has been provided alongside types of Places A and B are 100 km apart on a highway. One car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds, they meet in 5 hours. If they travel towards each other, they meet in 1 hour. What are the speeds of the two cars? theory, EduRev gives you an
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