**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:**

**STEP BY STEP SOLUTION**

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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