Zach is doing the following question:  A snail has fallen into a well. In order to climb out of the well, it climbs upwards by $8$ $\text{m}$ during the day. However, at night, it will slide down by $3$ $\text{m}$ . If the snail manages to climb out of the well on the $9$\textsuperscript{th}~day, after climbing $8$ $\text{m}$, how deep is the well?  His working is below:  $8 - 3 = 5$  $5\times 9 = 45$  The well is $45$ $\text{m}$ deep.  Is Zach correct? If not, show the correct working and answer. 
Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Snail Climbing out of Well Problems