 Hello and welcome to the session. In this session, we discuss the following question that says places A and B are 100 kilometers 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 5 hours. If they travel towards each other, they meet in one hour. What are the speeds of the two cars? Let's proceed with the solution now. We assume, let the speed of the car start from place A be equal to x kilometers per hour and let the car starting from place B be equal to y kilometers per hour. In the question, it's given that the places A and B are 100 kilometers apart. So we have distance between the places A and B is equal to 100 kilometers. In the question, we have two conditions when the cars travel in the same direction and when the cars travel towards each other. Now first, when the cars travel in the same direction, then the distance covered by the car starting from place A would be equal to speed into time and the speed is x kilometer per hour x into and time would be 5 hours. Since it's given in the question that when the cars travel in the same direction at different speeds, they meet in 5 hours. Covered by the car starting from place A would be equal to x into 5 that is equal to 5 x kilometers. Then the distance covered by the car from place B would be equal to speed into time and the speed for the car starting from place B is y kilometer per hour. So y into the time which is 5. So this is equal to 5 y kilometers. Now since places A and B are 100 kilometers apart, so we have 5 x minus 5 y is equal to 100 that is x minus y is equal to 20. Let this be equation 1. Now the next condition given in the question is when the cars travel towards each other, then the distance covered by the car from place A would be equal to speed into time. Speed in this case is x into time which is 1 hour as given in the question. So it would be x into 1 and this is equal to x kilometers. In the same way distance covered by the car from place B is equal to y which is the speed into time that is 1. So this is equal to y kilometers. Now A and B are 100 kilometers apart and the cars start from place A and place B and they move towards each other. So in this case we would have x plus y is equal to 100. Let this be equation 2. So now we have two equations x minus y equal to 20 and x plus y equal to 100. Now adding both these equations we get 2x is equal to 120. This gives us x is equal to 120 upon 2. Now 2, 60 times is 120 therefore we have x is equal to 60. Now substituting x equal to 60 in equation 2 we get 60 plus y is equal to 100 which gives us y is equal to 100 minus 60 that is equal to 40. Thus we get the value for y as 40. Thus we now have speed of the car is equal to 60 kilometers per of the car from place B is equal to 40 kilometers per hour. So this is our final answer. This completes the session. Hope you have understood the solution of this question.