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Two places A and B are 120 km apart from each other on a highway. A car start from A and another from B at the same time. If they move in same direction, they meet in 6 hours and if they move in opposite directions they meet in 1 hour and 12 minutes. Find the speeds of the car.?
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Two places A and B are 120 km apart from each other on a highway. A ca...
To find the speeds of the two cars, we can use the information provided about their meeting times in different scenarios.
Understanding the Problem
- Distance between A and B: 120 km
- Meeting time when moving in the same direction: 6 hours
- Meeting time when moving in opposite directions: 1 hour and 12 minutes (which is 1.2 hours)
Let the Speeds be
- Speed of the car from A: x km/h
- Speed of the car from B: y km/h
Equations from the Scenarios
1. Same Direction
When both cars move in the same direction, they meet after 6 hours. The distance covered by the faster car (which will reach the other car) will be:
- (x - y) * 6 = 120
- Therefore, x - y = 20 (Equation 1)
2. Opposite Directions
When they move towards each other, they meet after 1.2 hours. The combined distance they cover will equal 120 km:
- (x + y) * 1.2 = 120
- Therefore, x + y = 100 (Equation 2)
Solving the Equations
- From Equation 1: x - y = 20
- From Equation 2: x + y = 100
Now, add both equations:
(x - y) + (x + y) = 20 + 100
2x = 120
x = 60 km/h
Now, substituting x back into Equation 2:
60 + y = 100
y = 40 km/h
Final Speeds
- Speed of the car from A: 60 km/h
- Speed of the car from B: 40 km/h
This systematic approach allows you to determine the speeds of both cars using basic algebra.
Understanding the Problem
- Distance between A and B: 120 km
- Meeting time when moving in the same direction: 6 hours
- Meeting time when moving in opposite directions: 1 hour and 12 minutes (which is 1.2 hours)
Let the Speeds be
- Speed of the car from A: x km/h
- Speed of the car from B: y km/h
Equations from the Scenarios
1. Same Direction
When both cars move in the same direction, they meet after 6 hours. The distance covered by the faster car (which will reach the other car) will be:
- (x - y) * 6 = 120
- Therefore, x - y = 20 (Equation 1)
2. Opposite Directions
When they move towards each other, they meet after 1.2 hours. The combined distance they cover will equal 120 km:
- (x + y) * 1.2 = 120
- Therefore, x + y = 100 (Equation 2)
Solving the Equations
- From Equation 1: x - y = 20
- From Equation 2: x + y = 100
Now, add both equations:
(x - y) + (x + y) = 20 + 100
2x = 120
x = 60 km/h
Now, substituting x back into Equation 2:
60 + y = 100
y = 40 km/h
Final Speeds
- Speed of the car from A: 60 km/h
- Speed of the car from B: 40 km/h
This systematic approach allows you to determine the speeds of both cars using basic algebra.
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Two places A and B are 120 km apart from each other on a highway. A car start from A and another from B at the same time. If they move in same direction, they meet in 6 hours and if they move in opposite directions they meet in 1 hour and 12 minutes. Find the speeds of the car.?
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Two places A and B are 120 km apart from each other on a highway. A car start from A and another from B at the same time. If they move in same direction, they meet in 6 hours and if they move in opposite directions they meet in 1 hour and 12 minutes. Find the speeds of the car.? 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 Two places A and B are 120 km apart from each other on a highway. A car start from A and another from B at the same time. If they move in same direction, they meet in 6 hours and if they move in opposite directions they meet in 1 hour and 12 minutes. Find the speeds of the car.? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two places A and B are 120 km apart from each other on a highway. A car start from A and another from B at the same time. If they move in same direction, they meet in 6 hours and if they move in opposite directions they meet in 1 hour and 12 minutes. Find the speeds of the car.?.
Two places A and B are 120 km apart from each other on a highway. A car start from A and another from B at the same time. If they move in same direction, they meet in 6 hours and if they move in opposite directions they meet in 1 hour and 12 minutes. Find the speeds of the car.? 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 Two places A and B are 120 km apart from each other on a highway. A car start from A and another from B at the same time. If they move in same direction, they meet in 6 hours and if they move in opposite directions they meet in 1 hour and 12 minutes. Find the speeds of the car.? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two places A and B are 120 km apart from each other on a highway. A car start from A and another from B at the same time. If they move in same direction, they meet in 6 hours and if they move in opposite directions they meet in 1 hour and 12 minutes. Find the speeds of the car.?.
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Two places A and B are 120 km apart from each other on a highway. A car start from A and another from B at the same time. If they move in same direction, they meet in 6 hours and if they move in opposite directions they meet in 1 hour and 12 minutes. Find the speeds of the car.?, a detailed solution for Two places A and B are 120 km apart from each other on a highway. A car start from A and another from B at the same time. If they move in same direction, they meet in 6 hours and if they move in opposite directions they meet in 1 hour and 12 minutes. Find the speeds of the car.? has been provided alongside types of Two places A and B are 120 km apart from each other on a highway. A car start from A and another from B at the same time. If they move in same direction, they meet in 6 hours and if they move in opposite directions they meet in 1 hour and 12 minutes. Find the speeds of the car.? theory, EduRev gives you an
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