Q) Places A and B are 180 km apart on a highway. One car starts from A and another from B at the same time. If the car travels in the same direction at different speeds, they meet in 9 hours. If they travel towards each other with the same speeds as before, they meet in an hour. What are the speeds of the two cars?
Ans: Given the distance between A and B is 180 km
Let’s consider the speeds of cars as X and Y km/hr
By given first condition, they move in same direction,
hence resultant speed = (X – Y)
and they take 9 hours to meet, then 
∴ X – Y = 
∴ X – Y = 20 …… (i)
By given second condition, they move in opposite direction,
hence resultant speed = (X + Y)
and they take 1 hours to meet, then 
∴ X + Y = 
∴ X + Y = 180 …… (ii)
By adding both equations (i) & (ii), we get:
(X – Y) + (X + Y) = 20 + 180
∴ 2 X = 200
∴ X = 
= 100 km/hr
By substituting this value of X in equation (i), we get:
X – Y = 20
∴ (100) – Y = 20
∴ Y = 100 – 20 = 80 km/hr
Therefore, the speeds of the cars are 100 km/hr and 80 km/hr.
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