Question 1133213: A rabbit was 60 of her own leaps in front, while being chased by a dog, and took three leaps while the dog took two. But the dog went as far in three leaps as the rabbit did in seven.
In how many leaps did the dog catch the rabbit?
Answer by ikleyn(52775)   (Show Source):
You can put this solution on YOUR website! .
The rabbit makes 3 jumps at the same time as the dog makes 2 jumps.
Hence, the rabbit makes 9 jumps at the same time as the dog makes 6 jumps.
But 6 dog's jumps equate to 14 rabbit's jumps.
Hence, at the same time as rabbit makes 9 jumps, the dog moves forward for the distance of 14 rabbit's jumps.
Thus every time as the rabbit moves forward for his 9 jumps, the dog is in 5 = 14 - 9 rabbit's jumps closer to him.
It implies that as soon as the rabbit completes his 9*12-th jump (= 108-th jump), the dog will catch up the rabbit.
Notice 12 = 60/5.
Answer. As soon as the rabbit makes his 108-th jump, the dog will catch up the rabbit.
Or, in the terms of dog's jumps, as soon as the dog makes his 6*12 = 72-th jump, the dog will catch up the rabbit.
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To see other similar solved problem, look into the lesson
- A rabbit and a dog
in this site.
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