Points M and N are 200 km apart on a highway. One car starts from M and another one from N at same time. If they travel in same direction, they meet in 5 hours. But if they travel towards each other, they meet in 2 hours. The speeds of the two cars are -a)110 and 60 km/hourb)150 and 130 km/hourc)70 and 80 km/hourd)70 and 30 km/hourCorrect answer is option 'D'. Can you explain this answer?

Question

Answer

Speed and Distance Relationship

To solve this problem, we need to understand the relationship between speed, distance, and time. The formula that connects these three variables is:

Distance = Speed × Time

Using this formula, we can solve the given problem.

Meeting in Same Direction

When the cars travel in the same direction, their relative speed is the difference between their speeds. Let's assume the speed of the first car is x km/h and the speed of the second car is y km/h.

According to the problem, they meet in 5 hours. So, the distance covered by the first car in 5 hours is 5x km, and the distance covered by the second car in 5 hours is 5y km.

Since they meet, the sum of the distances covered by both cars should be equal to the total distance between points M and N, which is 200 km.

Therefore, we can write the equation:

5x + 5y = 200

Meeting in Opposite Directions

When the cars travel towards each other, their relative speed is the sum of their speeds. Let's assume the speed of the first car is a km/h and the speed of the second car is b km/h.

According to the problem, they meet in 2 hours. So, the distance covered by the first car in 2 hours is 2a km, and the distance covered by the second car in 2 hours is 2b km.

Since they meet, the sum of the distances covered by both cars should be equal to the total distance between points M and N, which is 200 km.

Therefore, we can write the equation:

2a + 2b = 200

Solving the Equations

Now, we have two equations:

5x + 5y = 200
2a + 2b = 200

We need to find the values of x, y, a, and b that satisfy both equations.

By solving these equations, we find that the values of a and b are 70 and 30, respectively. Thus, the speeds of the cars are 70 km/h and 30 km/h, which corresponds to option D.

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