The depth of 150 ft is 10 times taken the depth of 15 feet.


So the person shoud pay $9.00  per first 15 ft;

                   then $9.10  per next  15 ft;

                   then $9.20  per next  15 ft;

 . . . . . . . . . . . . . . . . . . . . . . . . 

                   and so on until $10.40 per the last 15 ft.


Thus uou need to find the sum 


    9.00 + 9.10 + 9.20 + . . . + 10.40  dollars.


This sequense is an arithmetic progression with the first term equal to 9.00;

with the common difference of 0.10 and the number of terms 15.


There are different formulas and several ways to find the sum.


          The simplest way for beginner students is to find 
          the average value of the progression and multiply it 
          by the number of terms in the progression.


In this case, the average value of the progression is half the sum of the first and the last terms 

     =  =  = 9.70  dollars;


So the total cost (the sum) is  9.70*15 = 145.50 dollars.


ANSWER.  $145.50.