Two cars travel from different locations at constant speeds. To meet each other after starting at the same time, they take 1.5 hours if they travel towards each other, but 10.5 hours if they travel in the same direction. If the speed of the slower car is 60 km/hr, then the distance traveled, in km, by the slower car when it meets the other car while traveling towards each other, is
Started 1 week ago by Shashank in
Explanatory Answer
Let the distance between the 2 cars be D km.
Let the speeds of the two cars be ‘a’ and ‘b’ respectively and a > b.
Case I)
Cars are moving in the opposite direction (towards each other)
Relative speed = a + b
Time taken = 1.5 hrs
Case II)
Cars are moving in the same direction (Car A chasing Car B)
Relative speed = a - b
Time taken = 10.5 hrs
In both the cases the distance between the cars is the same, ‘D’.
But the time taken is in the ratio 1.5 : 10.5 or 1 : 7
Therefore, the speeds will be in the ratio 7 : 1
a + b = 7(a - b)
8b = 6a
3a = 4b
Substituting b = 60 kmph,
We get, a = 80 kmph.
D = (a + b) * 1.5 = 210km
When they move towards each other the distance covered by them is in the ratio 4 : 3 and the total distance covered by them together is 210 km.
The slower car, B, covers 3/7 th of this 210 km which is 90 km.
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