A red ant is sitting on one side of the table(point X) and a black ant is sitting on the other side of the table(point Y). They decide on switching places and start walking towards each other in a straight line. On the way both ants meet and after that it takes 20 seconds for the red ant to move to point Y and 5 seconds for the black ant to move to point X . Find the total time taken by the red ant and the black ant individually to make their journey.

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Solution

Let the speed of red ant be R.
Speed of Black ant be B.
Time at which they cross their paths be T.

Now we will apply the basic formula of distance
Distance = Speed * Time

The Red ant travels R * T distance before meeting and R * 20 after meeting.
The Black ant travels B * T distance before meeting and B * 5 after meeting.

Now as per the question,
The distance traveled by red ant before they both meet will be equal to the distance covered by black ant after they meet. We can say the same for the vice versa case as well.

Thus
R * T = B * 5 and B * T = R * 20

Using both the quations
T = 10

Thus the red ant will require 10 + 20 = 30 seconds to travel the distance.
And the black ant will take 10 + 5 = 15 seconds to travel the distance.

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