Q. 154.1( 8 Votes )

Places A and B ar

Answer :

Let the speed of first car be x km/hr


And the speed of the second car be y km/hr


Given A and B are 80km apart,



a car starts from A and another from B at the same time


Case 1: moving in same direction


The two cars will meet in 8 hours, so


time = 8hrs


Let the two cars meet at point C, so



So, distance travelled by first car = AC


And distance travelled by second car = BC


So, the difference of distance travelled = AC - BC


AB = 80km is the relative distance


Relative speed will be speed of 1st car - speed of 2nd car


speed = (x - y) km/h


And we know


Distance = speed × time


Substituting the values, we get


80 = (x - y) × 8


x - y = 10……….(i)


Case 2: moving in opposite direction


The two cars will meet in 1 hour 20 minutes, so






Let the two cars meet at point C, so



So, distance travelled by first car = AC


And distance travelled by second car = BC


So the total distance travelled = AC + BC


AB = 80km is the relative distance


Relative speed will be speed of 1st car + speed of 2nd car


speed = (x + y) km/h


And we know


Distance = speed × time


Substituting the values, we get




x + y = 60………(ii)


So, the pair of linear equations in two variables are


x + y = 60


x - y = 10


Now we will solve these pair of equations,


Adding the two equations we get


x + y = 60


x - y = 10


2x = 70


x = 35


Hence the speed of first car is 35 km/hr


Substituting the value of x in first equation, we get


x + y = 60


35 + y = 60


y = 60 - 35


y = 25


Hence the speed of second car is 25 km/hr.


So, the speed of two cars is 35km/hr and 25km/hr.


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