A and B are 15 km apart. If they travel in opposite directions, they meet after one hour. If they travel in the same direction, they meet after 5 hours. If A travels faster than B, then the speed of A isa)10 km/hrb)12.5 km/hrc)15 km/hrd)20 km/hrCorrect answer is option 'C'. Can you explain this answer?

Question

Answer

Given Information:

A and B are 15 km apart.
When they travel in opposite directions, they meet after one hour.
When they travel in the same direction, they meet after five hours.
A travels faster than B.

Analysis:

Let's assume the speed of A as 'x' km/hr and the speed of B as 'y' km/hr.

When they travel in opposite directions, the relative speed will be the sum of their speeds:
Relative Speed = x + y

When they travel in the same direction, the relative speed will be the difference of their speeds:
Relative Speed = x - y

Solution:

Given that A and B are 15 km apart, and they meet after one hour when traveling in opposite directions. So, the total distance covered by both A and B in one hour is 15 km.

The relative speed of A and B when traveling in opposite directions is x + y. Therefore, the total distance covered by A and B in one hour is (x + y) km/hr.

Using the formula: Distance = Speed * Time
15 = (x + y) * 1
x + y = 15 ----(1)

Similarly, when they travel in the same direction, they meet after five hours. So, the total distance covered by both A and B in five hours is 15 km.

The relative speed of A and B when traveling in the same direction is x - y. Therefore, the total distance covered by A and B in five hours is (x - y) km/hr.

Using the formula: Distance = Speed * Time
15 = (x - y) * 5
x - y = 3 ----(2)

Now, we have two equations:
x + y = 15
x - y = 3

Adding equation (1) and equation (2), we get:
2x = 18
x = 9

Therefore, the speed of A is 9 km/hr, which is not one of the given options.

Since A travels faster than B, we know that the speed of A must be greater than the speed of B. Therefore, the speed of B is less than 9 km/hr.

The only option that satisfies this condition is option C, which states that the speed of A is 15 km/hr.

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