Question 182
a) A worm always walks on a straight line. Every day, it advances $5\ \mathrm{m}$ and retreats $3\ \mathrm{m}$. At the end of $15$ days, the worm will be at what distance from the starting point?
b) At the end of these $15$ days, how many meters will this worm walk in total?
c) Another worm also walks on a straight line, but in a different way than the first. On the first day, it moves $1\ \mathrm{m}$ forward and $1/2\ \mathrm{m}$ backwards. On the second day, it moves $1/2\ \mathrm{m}$ forward and $1/3\ \mathrm{m}$ backwards. On the third day, she walks $1/3\ \mathrm{m}$ forward and $1/4\ \mathrm{m}$ backwards, and so on. How many meters will it have walked after $1000$ days?
d) Someday this second worm will be able to be $2\ \mathrm{m}$ away from the starting point?
b) At the end of these $15$ days, how many meters will this worm walk in total?
c) Another worm also walks on a straight line, but in a different way than the first. On the first day, it moves $1\ \mathrm{m}$ forward and $1/2\ \mathrm{m}$ backwards. On the second day, it moves $1/2\ \mathrm{m}$ forward and $1/3\ \mathrm{m}$ backwards. On the third day, she walks $1/3\ \mathrm{m}$ forward and $1/4\ \mathrm{m}$ backwards, and so on. How many meters will it have walked after $1000$ days?
d) Someday this second worm will be able to be $2\ \mathrm{m}$ away from the starting point?