Simply divide the two fractions:
3 2/3 ÷ 1/3

But we must make the Mixed fraction into an improper fraction so that it will become 11/3
11/3 ÷ 1/3

we must follow the dividing rule, of course... therefore, we will multiply 11/3 to the reciprocal of 1/3 which is 3/1.. Therefore,
11/3 × 3/1 = 33/3

Reduce it to lowest term, then it will become 11. But still, 11 isn't the final answer. Why? Let me explain.

Based on your word problem, the group of hikers marked their start (beginning of their hike) and their final destination (end of their hike). Therefore, we must add 2 to 11:
11 + 2 = 13

Therefore, the answer to your question is 13.

Simple as that. ☺
Hope it helped ☺
There are only 12 markers. First mark is the origin (zero) last mark is the end of their hike at 3 and 2/3 km. You can visualize by drawing a number line, then mark Zero (origin), mark every third up to 3 2/3 , and you have 12 markers. 
Thanks for your correction. Sorry for the wrong answer anyway. Also, just realize that when I divide 3 2/3 by 1/3 the last mark will be included. Thanks MomGie ☺
Actually, i also thought of adding 2, hehe:-) But, when I read again, I had to validate using  the number line :-) Don't worry, we all mistakes. You're still one of the credible and reliable  answer givers here:-) 
Well, thank you.☺
  • Brainly User
Divide the total distance hiked (3 ²/₃ km) by 1/3, then add 1 for the first marker at the beginning.

Follow the rule in dividing factions:  Multiply the dividend by the reciprocal of its divisor.  Change the mixed number dividend to improper fraction, then proceed to multiplication.

Let the number of markers be x.

x = (11/3  ×  3/1) + 1 
x = (11) + 1
x = 12

ANSWER:  The hikers could have counted 12 markers.

(Please click image below for visual explanation.)