# Please help me with this math problem!?

Nicole 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 four hours, find (a)how long she jogged and (b) the total distance she traveled.

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if Nicole jogs for 1 hour she will travel 7.2 miles, if she walks back back at a rate of 2.4 miles per hour it will take 3 hours to reach her start position (2.4*3=7.2 miles)

jog time + walk time = 1 + 3 =4

a) jog for 1 hour

b) distance travel =7.2 + (2.4*3)= 14.4 miles

Since Nicole jogged and walked the same distance, the equation is going to be equal. use “x” as the jogging time and “y” as the walking time. So the equation is going to be 7.2x=2.4y. We will be needing another equation to solve this problem. Since the total amount of time is 4 hours, we can say that X+Y=4.

So the two equations would be

7.2x-2.4y=0(since you subtracted 2.4y from both sides)

and

X+Y=4

We combine the two equations by cancelling out one variable by adding.

7.2x-2.4y+2.4x+2.4y=0+9.6

Then the equation should end out as

9.6x=9.6

We divide 9.6 from both equations so

x=1 hour

Then plug “1” in X+Y=4, so then 1+Y=4

Then Y=3 hours

b)plug 1 and 3 in 7.2x=2.4y

which comes out as 7.2=7.2

So,Nicole jogged 7.2 miles

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