A hare pursued by a grey hound is 50 of her own leaps before him. while the hare takes 4 leaps, the grey hound takes 3 leaps. In one leap, the hare goes 1.75 metres and the grey hound 2.75 metres. In how many leaps, will the grey hound overtake the hare?
A hare pursued by a grey hound is 50 of her own leaps before him. while the hare takes 4 leaps, the grey hound takes 3 leaps. In one leap, the hare goes 1.75 metres and the grey hound 2.75 metres. In how many leaps, will the grey hound overtake the hare? Correct Answer 211 leaps
Given:
Grey hound and hare make 3 leaps and 4 leaps respectively. This happens at the same time.
The greyhound goes 2.75 metres in one leap.
The hare goes 1.75 metres in 1 leap.
Calculation:
The hare goes in 4 leaps = 4 × 1.75
⇒ 7 metres
The greyhound goes in 3 leaps = 3 × 2.75
⇒ 8.25 metres
Distance gained by grey hound = (8.25 – 7) = 1.25 metres
Distance covered by hare in 50 leaps = 50 × 1.75
= 87.5 meters
Now, 1.25 metres is gained by greyhound in 3 leaps
so, 87.5 metres is gained in = (3/1.25) × 87.5
⇒ 210 leaps
It will take 210 jumps to catch the hare but to overtake it, it must take one step more
∴ 211 steps will be the correct answer.
Mistake Points
Please see the last line, it is asked how many leaps to overtake the hare, not catching the hare.
It will take 210 jumps to catch the hare but to overtake it, it must take one step more. thus 211 steps will be the correct answer.
