Two men A and B start with velocities v at the same time from the junction of two roads inclined at `45^@` to each other. If they travel by different roads, find the rate at which they are being separated.

Form the pair of linear equations In the following problems and find their solutions (if they exist) by any algebraic method. :- Places A and B are 100 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 5 hours. If they travel towards each other, they meet in 1 hour. What are the speeds of the two cars ?

Suppose you want to minimise the waiting time of vehicles at a traffic junction of four roads. Which of these factors are important and which are not? (i) Price of petrol. (ii) The rate at which the vehicles arrive in the four different roads. (iii) The proportion of slow-moving vehicles like cycles and rickshaws and fast moving vehicles like cars and motorcycles.

Two trains leave a railway station at the same time. The first train travels due west and the second due north. The first train travels 5 km/hr faster than the second train. If after two hours, they are 50 km apart, find the average speed of each train.

A and B are two points of 150 km apart on a highway. A car starts from A and another from B at the same time. If they move in the same direction, they meet in 15 hours, but if they move in opposite direction, they meet in one hour. Find their speeds.

Form the pair of linear equations in the following problems and find their solutions (if they exist) by any algebraic method :-Places A and B are 80 km apart from each other on a highway. A car starts from A and another from B at the same time. If they move in the same direction they meet in 8 hours , and if they move in opposite direction, they meet in 1 hour and 20 minutes respectively. Find the speed of the cars.

Two cars are 351 km apart. They start at the same time and drive towards each other. One travels at 70 km/hr and the other travels at 65 km/hr. How much time do they take to meet each other?

Two boatmen start simultaneously from the opposite shore of a river with same speed and they cross eachother after 45 minutes of their starting from the respective shores. They rowed till theyreached the opposite shore and returned immediately after, reaching the shores. When willthey cross each other again?

Street Plan : A city has two main roads which cross each other at the centre of the city. These two roads are along the North-South direction and East-West direction. All other streets of the city run parallel to these roads and are 200 m apart. There are about 5 streets in each direction. Using 1 cm = 200 m, draw a model of the city on your notebook. Represent roads/ streets by single lines. There are many cross-streets in your model. A particular cross-street is made by two streets, one running in the North - South direction and another in the East - West direction. Each cross street is referred to in the following manner : the 2^(nd) street running in the North -South direction and 5^(th) in the East - West direction meet at some crossing, then we will call this crossstreet (2, 5). Using this convention find : how many cross-streets can be referred to as (4, 3).

Street Plan : A city has two main roads which cross each other at the centre of the city. These two roads are along the North-South direction and East-West direction. All other streets of the city run parallel to these roads and are 200 m apart. There are about 5 streets in each direction. Using 1 cm = 200 m, draw a model of the city on your notebook. Represent roads/ streets by single lines. There are many cross-streets in your model. A particular cross-street is made by two streets, one running in the North - South direction and another in the East - West direction. Each cross street is referred to in the following manner : the 2^(nd) street running in the North -South direction and 5^(th) in the East - West direction meet at some crossing, then we will call this crossstreet (2, 5). Using this convention find : how many cross-streets can be referred to as (3, 4).