Given that Julia ran and bike for a total of 40 miles in 5.8 hours.
Let x be the running time and y be the biking time.
So, x+y=5.8
y = 5.8 -x ,this is our first equation.
We are also given that average running speed of Julia = 5.5 mph
Distance ran by Julia in x hours = speed * time =5.5x
Given average biking speed of Julia = 13.5mph
Distance covered by biking in y hours = speed* time = 13.5 y
So total distance covered by julia = 5.5x+13.5y
But given this distance is 40 miles.
That is 5.5x+13.5y = 40
Let us plugin first equation in above step.
5.5x+13.5(5.8-x) = 40
5.5x+78.3-13.5x = 40
78.3-8x = 40
8x = 78.3-40 = 38.3
[tex]x=\frac{38.3}{8} = 4.7875 hours[/tex] = 4.8 hours
let us plugin this in our first equation
y= 5.8-x = 5.8-4.7875 = 1.0125 hours = 1.0 hours
a) Julia ran for 4.8 hours
b) Julia biked for 1.0 hours
