Page 11 - LN

When the cars travel in the same direction, they meet at P(say) after 7 hours.

Distance covered by first car = AP = (7x) km [since, distance = time speed]
Distance covered by second car = BP = 7y km

AP - BP = AB
7x - 7y = 70
x - y = 10 ………..(1) [dividing throughout by 7]

When the cars travel towards each other, they meet at Q(say) after 1 hour
st
Distance covered by 1 car
= AQ = x km
nd
Distance covered by 2 car = BQ = y km

AQ + BQ = AB
x + y = 70 ……. (2)

Adding equation (1) and (2), we get,

Substituting the value of x in (1), we get,
40 - y = 10
-y = 10 - 40 = -30
y = 30
The speed of the car which starts from point A is 40 km/hr and the car which starts from
B is 30 km/hr

Special Method: This method is applicable only when a 1 = b 2 and a 2 = b 1 or a 1 =
- b 2 and a 2 = - b 1 .

Step 1- Add the two equations and then divide the equation by the common factor of
the coefficients to get the value of x + y or x - y

Step 2 – Subtract one equation from the other and then divide the equation by the
common factor of the coefficients to get the value of x – y or x + y

Step 3- Solve the equation in two variables to obtain the solutions.

11