Question

An athlete is able to jump FOREVER. However, every time she jumps (Long Jump) she gets a bit more tired, and every jump goes 1/2 as far as her prior jump. Now, for her very first jump, she goes 1/2 of a foot. On her second jump, she goes ¼ of a foot, and so on and so forth. How many jumps does it take for her to travel 1 foot? Show Process by using a number line.

Answer 1

So, as per the question she starts with 1/2 foot distance, and her ability reduces by 1/2 factor for each step she takes
Now,
The distance covered can be defined in the form of geometric series as,
1/2 + 1/4+  1/8+  1/16 ...
Now,
Sum of an GP for r<1 is
S=a(1- r^n)/(1-r)
So, she has to complete 1 foot no matter how many number of steps she takes
Also,
S∞ = a/(1-r)
Now,
a=1/2 r=1/2
So,
S∞ = 1
By this we conclude that she has to take infinite number of steps to complete a distance of 1 foot
(It was also mentioned in the question that she can run forever)
So,if we want to represent it on number line one end will be a point starting on 1/2 the other end will be arrow tending to ∞

Answer 2

Answer:

Not possible.

The given data shows that the athlete started travelling from a ½ foot. For every next jump it will become half of previous jump

For example        

$\frac {1} {2} + \frac {1} {4} + \frac {1} {8} + \frac {1} {16} ------ + infinite = 1$

For first step it become $\frac {1} {2}$

Second step it become $\frac {1} {4}$

and so, on

Since, she travels half of the previous jump it is not possible to reach 1 foot.