Mike is 7.5 miles ahead of julia running at 5.5 miles per hour and julia is running at the speed of 6 miles per hour. How long does it take julia to catch mike.

The answer is 15 hours but I am unsure as to why, can someone explain?

15 hours.

Step-by-step explanation:

Suppose the time taken to catch Mike is t hours and the distance ran by Mike is x miles then

5.5 = x / t (Mike) - - - ... (1)

6 = (x + 7.5) / t (Julia) ... (2)

From equation (1):

x = 5.5t ... (3).

From equation (2):

x + 7.5 = 6t

x = 6t - 7.5 ... (4).

Eliminating x from equations 3 and 4:

6t - 7.5 = 5.5t

0.5t = 7.5

t = 15 hours.