Question

A giant rabbit is tied to a pole in the ground by an infinitely stretchy elastic cord attached to its tail. A hungry flea is on the pole watching the rabbit. The rabbit sees the flea, jumps into the air and lands one mile from the pole (with its tail still attached to the pole by the elastic cord). The flea gives chase and leaps into the air landing on the stretched elastic cord one inch from the pole. The rabbit, seeing this, again leaps into the air and lands another mile away from the pole (i.E., a total of two miles from the pole). Undaunted, the flea bravely leaps into the air again, landing on the elastic cord one inch further along. Once again the rabbit jumps another mile and the flea jumps another inch along the cord. If this continues indefinitely, will the flea ever catch up to the rabbit?

Answer 1

Answer:

YES - Flea would be able to catch up

Step-by-step explanation:

When rabbit is at 1 mile

Flea is at 1 inch on cord = 1/63360 mile

Distance between them = 1 mile - 1/63360

When Rabbit jumps again 1 mile

The cord is stretched both sides of rabbit

let say x mile is stretched toward pole then 1-x mile toward rabit

so now distance between rabbit & flea

2-x - (1/63360 + x)

and flea further move inch = 1/63360 mile

so ditance

2 - 2x - 2/63360 mile

similarly on the next mile jump stretch portion toward pole will increase

and it will keep reducing  increase in distance

and at some time stretching toward pole will be more than stretch toward rabbit

then Distance will keep reducing and finally flea will catch up