Jean runs 8 mi and then rides 11 mi on her bicycle on a biathlon. she rides 9 mph faster than she runs. if the total time for her to complete the race is 1.5 hr, determines her speed running and her speed riding her bicycle.

Let Jean's speed while running = x mph

Then Jean's speed while riding will be = x+9 mph

Distance covered by running = 8 miles

Distance covered by riding = 11 miles

Total time taken to complete the race = 1.5 hours

As,

So, time for running=

And time for riding=

Equation becomes:

Now, multiply every term by 2x(x+9) to clear denominators:  

Simplifying it we get

Solve the quadratic equation using formula

putting a=3 , b= -11, c= -144

we get (x - 9)(3x + 16) = 0

where x=9 and x=

Neglect the negative answer as speed cannot be negative, so x = 9 mph

Hence, Jean's running speed is 9 mph and riding speed is x+9 = 9+9 = 18 mph

heyyy

step-by-step explanation: