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V) Places A and B are 80 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 8 hours. If they travel towards each other, they meet in 1.2 hour. What are the speeds of the two cars?
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V) Places A and B are 80 km apart on a highway.One car starts from A a...
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V) Places A and B are 80 km apart on a highway.One car starts from A a...
Given Information:
- Distance between places A and B = 80 km
- Time taken for the cars to meet when traveling in the same direction = 8 hours
- Time taken for the cars to meet when traveling towards each other = 1.2 hours
Approach:
Let's assume the speed of the car starting from A as "x" km/h and the speed of the car starting from B as "y" km/h. We will use the formula Distance = Speed * Time to solve this problem.
When the cars travel in the same direction:
When the cars travel in the same direction, the relative speed of the cars is the difference between their speeds. So, the relative speed of the cars is (x - y) km/h.
The distance covered by the cars in 8 hours is 80 km. Therefore, the equation becomes:
(x - y) * 8 = 80
When the cars travel towards each other:
When the cars travel towards each other, the relative speed of the cars is the sum of their speeds. So, the relative speed of the cars is (x + y) km/h.
The distance covered by the cars in 1.2 hours is 80 km. Therefore, the equation becomes:
(x + y) * 1.2 = 80
Solving the equations:
Let's solve these two equations to find the values of x and y.
Equation 1: (x - y) * 8 = 80
Expanding the equation, we get:
8x - 8y = 80
Equation 2: (x + y) * 1.2 = 80
Expanding the equation, we get:
1.2x + 1.2y = 80
Now, we have a system of linear equations. We can solve these equations simultaneously to find the values of x and y.
Solution:
Using the method of elimination, we can eliminate y from the equations. Multiplying equation 1 by 1.2 and subtracting it from equation 2, we get:
1.2x + 1.2y - (0.96x - 0.96y) = 80 - 96
0.24x + 2.16y = -16
Simplifying the equation, we get:
0.24x + 2.16y = -16
Dividing the equation by 0.24, we get:
x + 9y = -66.67
Now, we have the following system of equations:
8x - 8y = 80
x + 9y = -66.67
Solving these equations using any suitable method (such as substitution or elimination), we can find the values of x and y, which will give us the speeds of the two cars.
- Distance between places A and B = 80 km
- Time taken for the cars to meet when traveling in the same direction = 8 hours
- Time taken for the cars to meet when traveling towards each other = 1.2 hours
Approach:
Let's assume the speed of the car starting from A as "x" km/h and the speed of the car starting from B as "y" km/h. We will use the formula Distance = Speed * Time to solve this problem.
When the cars travel in the same direction:
When the cars travel in the same direction, the relative speed of the cars is the difference between their speeds. So, the relative speed of the cars is (x - y) km/h.
The distance covered by the cars in 8 hours is 80 km. Therefore, the equation becomes:
(x - y) * 8 = 80
When the cars travel towards each other:
When the cars travel towards each other, the relative speed of the cars is the sum of their speeds. So, the relative speed of the cars is (x + y) km/h.
The distance covered by the cars in 1.2 hours is 80 km. Therefore, the equation becomes:
(x + y) * 1.2 = 80
Solving the equations:
Let's solve these two equations to find the values of x and y.
Equation 1: (x - y) * 8 = 80
Expanding the equation, we get:
8x - 8y = 80
Equation 2: (x + y) * 1.2 = 80
Expanding the equation, we get:
1.2x + 1.2y = 80
Now, we have a system of linear equations. We can solve these equations simultaneously to find the values of x and y.
Solution:
Using the method of elimination, we can eliminate y from the equations. Multiplying equation 1 by 1.2 and subtracting it from equation 2, we get:
1.2x + 1.2y - (0.96x - 0.96y) = 80 - 96
0.24x + 2.16y = -16
Simplifying the equation, we get:
0.24x + 2.16y = -16
Dividing the equation by 0.24, we get:
x + 9y = -66.67
Now, we have the following system of equations:
8x - 8y = 80
x + 9y = -66.67
Solving these equations using any suitable method (such as substitution or elimination), we can find the values of x and y, which will give us the speeds of the two cars.
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V) Places A and B are 80 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 8 hours. If they travel towards each other, they meet in 1.2 hour. What are the speeds of the two cars?
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V) Places A and B are 80 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 8 hours. If they travel towards each other, they meet in 1.2 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 V) Places A and B are 80 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 8 hours. If they travel towards each other, they meet in 1.2 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 V) Places A and B are 80 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 8 hours. If they travel towards each other, they meet in 1.2 hour. What are the speeds of the two cars?.
V) Places A and B are 80 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 8 hours. If they travel towards each other, they meet in 1.2 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 V) Places A and B are 80 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 8 hours. If they travel towards each other, they meet in 1.2 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 V) Places A and B are 80 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 8 hours. If they travel towards each other, they meet in 1.2 hour. What are the speeds of the two cars?.
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V) Places A and B are 80 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 8 hours. If they travel towards each other, they meet in 1.2 hour. What are the speeds of the two cars?, a detailed solution for V) Places A and B are 80 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 8 hours. If they travel towards each other, they meet in 1.2 hour. What are the speeds of the two cars? has been provided alongside types of V) Places A and B are 80 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 8 hours. If they travel towards each other, they meet in 1.2 hour. What are the speeds of the two cars? theory, EduRev gives you an
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