I need solving this

Question

Nautical speed was once measured by throwing a rope into the water from the ship. The rope had knots every 47 ft 3 in, and its wedge-shaped end would "grab" the water. The speed was the number of rope knots that went into the water while a 28-second hourglass ran down. A nautical mile is about 6076 feet. What is the ratio of a nautical mile to the length of the rope between knots?

Answer 1

This problem has some interesting TMI (too much information).

 

After understanding the problem, we may reduce it to, "What is the ratio of 6076 feet to 47 feet 3 inches?"

 

To convert units without converting value, we use the Multiplicative Identity (that is, 1).  This problem uses:

    1 = (1 ft)/(12 in)

 

What is ratio of   6076 feet to 47 feet 3 inches ?

                         6076 feet to 47.25 feet              [3 in is 3*(1/12) ft = 1/4 ft]

                         607600 : 4725

      2*2*2*2*5*5*7*7*31 : 3*3*3*5*5*7              [prime factors]

           2*2*2*2*7*31 : 3*3*3                          [delete duplicates to reduce]

                       3472 : 27