-
A hare sees a dog 100 metres away from her and scuds off in the opposite direction at a speed of 12 km per hr. A minute later the dog perceives her and chases her at a speed of 16 km per hr. How soon will the dog overtake the hare and at what distance from the spot when the hare took flight?
-
- 900 metres
- 950 metres
- 1000 metres
- 1100 metres
Correct Option: D
Let the hare at B sees that dog is at A.
∴ AB = 100 metres
Again, let C be the position of the hare when the dog sees her.
∴ AB = 100 metres
Again, let C be the position of the hare when the dog sees her.
∴ BC= the distance covered by the hare in 1 minute
| = | = 200 metres | |
| 60 |
∴ AC = AB + BC
= 100 + 200 = 300 metres
Thus, hare has a start of 300 metres.
Now, the dog gains 16 – 12 = 4 kms
4000 metres in 1 hour i.e. 60 minutes
∴ The distance gained by dog in 1 minute
| = | = | metres | ||
| 60 | 3 |
| ∵ | metres is covered in 1 minute | |
| 3 |
∴ 300 metres is covered in
| = | minutes | ||
| 200 | 2 |
| Again the distance walked by hare in | minutes | |
| 2 |
| = | × | = 900 metres | ||
| 60 | 2 |
∴ Total distance from
B = 200 + 900 = 1100 metres.
