Answer:
Dave's running speed for the first 9 miles is 6 miles per hour
Step-by-step explanation:
Let
x ----> Dave's running speed for the first 9 miles in miles per hour
Remember that
The speed is equal to divide the distance by the time
so
The time is equal to divide the distance by the speed
so
The time in the first nine miles plus the time in the other five miles (14-9=5 miles) must be equal to 2 hours
[tex]\frac{9}{x}+\frac{5}{x+4}=2[/tex]
solve for x
Multiply by x(x+4) both sides
[tex]9(x+4)+5x=2x(x+4)[/tex]
[tex]9x+36+5x=2x^2+8x[/tex]
[tex]2x^2-6x-36=0[/tex]
solve the quadratic equation by graphing
The solution is x=6
see the attached figure
therefore
Dave's running speed for the first 9 miles is 6 miles per hour
