A cat chasing a rabbit which has a start of 45m, jumps 3m every time the rabbit jumps 2m. In how many leaps does the cat overtake the rabbit?
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Let x be the number of jumps taken
The cat jumps 3m every time the rabbit jums 2m
==> 3x the number of jumps for the cat
==> 2x the number of meters for the rabbit
Also given that they start at 45m apart
==> 3x = 45 + 2x
Now let us subtract 2x from both sides:
==> x = 45
==> Then the cat will need to jump 45 jumps to catchup with the rabbit
The initial distanc between the rabbit and the cat is 45m.
The the distance covered by the cat in each jump = 3m. the distance covered by the rabbit is 2 m.
So after x jumps the distance between the cat and rabbit d = 2x+45 -3x. Or
d =2x +45-3x.
If the cat overtakes the rabbit, the d < 0. Or
2x+45-3x < 0.
45 < 3x-2x
45 < x.
So in the 45 th jump the cat covers 45*3 = 135m . The rat covers 45*2 = 90. Ao the the distance between them is 2*45+45 - 3*45 = 0.
So it is the 46 th jump that the cat goes ahead by 3*46-(2*46+45) = 138-137 = 1m .
This question can also be solved in a much simpler way.
The fact that cat jumps 3 m every time the rabbit jumps 2 m, means that the lead of rabbit over cat is reduced by 1 m (= 3 - 2) for every jump by the cat.
As the total lead is 45 meters the cat will cover all the lead and will be abreast with the rabbit immediately after the 45th leap. It will then overtake the rabbit on 46th leap.
Thus the answer is:
Cat will overtake the rabbit in 46 leaps.
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