Question

a car and a motorcycle start from the same spot and move in the opposite direction. after 2 hours the distance between them is 140 km. if they had travelled in the same direction, then the distance between them would have been 20 km after 2 hours. find the speed of the car and the motorcycle.

Answer 1

Consider a point 'X' from where the car and the bike have started. 

1) When travelling in opposite directions, let us suppose the distance travelled by the car from 'X' is 'A' and distance travelled by the bike from 'X' is 'B'.

  (Car is here)---------------------------X------------------------------(Bike is here)

 So, according to the question A+B=140 after two hours.

2) When travelling in same directions, let us take the same variables 'A' and 'B'.

Distance from 'X' to Car is 'A' and 'X' to Bike is 'B'.
 
X-------------------------------(Bike is here)--------------------------(Car is here).

So, A-B =20

Now we have 2 equations => A+B =140
                                                   A-B = 20
We get, distance travelled by car i.e. A = 80 and distance by bike B = 60 for 2 hrs. 
speed =(distance/time)
Speed of car(A) = 80/2 = 40 Km/hr.
Speed of bike(B) = 60/2 = 30 Km/hr.