Places A and B are 80 km apart from each other on a highway. One car starts from A and another from B at the same time. If they move in the same direction, they meet in 8 hours and if they move in opposite directions, they meet in 1 hour and 20 minutes. Find speed of the cars.
Let the speed of car I = x km/hr
And the speed of car II = y km/hr
Car I starts from point A and Car II starts from point B.
Let two cars meet at C after 8h.
Distance travelled by car I in 8h = 8x km
Distance travelled by car II in 8h = 8y km
Since, they are travelling in same direction, sign should be negative
8x – 8y = 80
⇒ x –y = 10 …(i)
Now, Let two cars meet after 1hr 20 min
1hr 20min 
Since they are travelling in opposite directions, sign should be positive.
⇒ 4x + 4y = 240
⇒ x + y = 60 …(ii)
On adding (i) and (ii) , we get
x – y + x + y = 10 + 60
⇒ 2x = 70
⇒ x = 35
Putting the value of x = 25 in Eq. (i), we get
35 – y = 10
⇒ y = 25
So, the speed of the two cars are 25km/h and 15 km/hr respectively.
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