SOLUTION: Jogging: Nicolle Ryba jogged for a distance and then turned around and walked back to her starting point. While jogging she averaged 7.2 miles per hour, and while walking she ave

Question 27291: Jogging: Nicolle Ryba jogged for a distance and then turned around and walked back to her starting point. While jogging she averaged 7.2 miles per hour, and while walking she averaged 2.4 miles per hour. If the total time spent jogging and walking was 4 hours, find
a) how long she jogged, and
b) the total distance she traveled
Thanks for any help. I've been trying to figure out how to set this up for 3 hours. I've tried to add the two rates and divide that by 4 but that didn't work. Am I on the right track?

Answer by sdmmadam@yahoo.com(530) (Show Source): You can put this solution on YOUR website!
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.

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