A rabbit gives 5 jumps at the same time that the dog that chases it gives 4, but 8 dog leaps equate in distance to 11 jumps of the rabbit.
If the rabbit takes 66 advantage jumps, how many jumps should the dog give to reach the rabbit?
Solution
The rabbit makes 5 jumps at the same time as the dog makes 4 jumps.
Hence, the rabbit makes 10 jumps at the same time as the dog makes 8 jumps.
But 8 dog's jumps equate to 11 rabbit's jumps.
Hence, at the same time as rabbit makes 10 jumps, the dog moves forward for the distance of 11 rabbit's jumps.
Thus every time as the rabbit moves forward for its 10 jumps, the dog is in 1 rabbit's jump closer to him.
It follows that as soon as the rabbit completes his 660-th jump, the dog will catch up the rabbit.
Answer. As soon as the rabbit makes his 660-th jump, the dog will catch up the rabbit.
