Question

1. Julia ran and bikes for a total of 40 miles in 5.8 hours. Her average running speed was 5.5 mph. Her average biking speed was 13.5 mph. Let x = total hours Julia ran Ley y = total hours Julia biked Use substitution to solve for x and y. SHOW ALL WORK. Round answers to nearest tenth. a) How many hours did Julia run? b) How many hours did Julia bike?

Answer 1

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

$x=\frac{38.3}{8} = 4.7875 hours$ = 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