Question 27291
Nicolle Ryba jogged for a distance and then turned around and walked back to her starting point means if she has jogged say y miles than she has walked back exactly y miles.
Her jogging speed is 7.2 miles per hour.
That is she covers 7.2 miles in one hour
which means she covers 1 mile in 1/7.2 of an hour.
Therefore she will jog y miles in (1/7.2)X y hours = y/7.2 hours
  (one divided by 7.2 then multiplied by y)
Her walking  speed is 2.4 miles per hour.
That is she covers 2.4 miles in one hour
which means she covers 1 mile in 1/2.4 of an hour.
Therefore she will walk y miles in (1/2.4)X y hours = y/2.4 hours
Total time for jogging plus walking is 4 hours
which means y/7.2 + y/2.4 = 4
The LCM(least common multiple of 7.2 and 2.4 is 7.2 (as 3 times 24 is 72)
Multiplying through out by 7.2
we get y + 3y = 4X 7.2
4y =4X7.2
Dividing by 4
y = 7.2
She has jogged for 7.2 miles (that means she has taken exactly 1 hr jogging)
and she has walked an equal distance(which means she has taken 3 hrs walking)
She has travelled 7.2 + 7.2 miles = 14.4 miles.