Places A and B are 100 km apart on a highway. One car starts from A and another from B at the same time.

Question

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 ?

Answer 1

Distance between places A and B is 100 km. 

Speed of A car us ‘u’ km/hr. 

Speed of B car is ‘v’ km/hr. 

If the cars travel in the same direction at different speeds they meet in 5 hours about 20 km. 

∴ u – v = 20 ………. (i) 

If the cars travel in the same direction, total distance covered =100 km. 

∴ u + v = 100 …….. (ii) 

We can solve by Elimination method: 

From eqn. (i) + eqn. (ii),

∴ u = 60 km/hr. 

Substituting the value of ‘u’ in eqn. (ii), 

u + v = 100 

60 + v = 100 

v = 100 – 60 

v = 40 km/hr. 

∴ u = 60 km/hr. 

v = 40 km/hr.