Question

Dave is training for a big race. Today, he ran 14 miles in 2 hours. After running the first nine miles at certain speed, he increases his speed by 4 miles per hour. What is Dave's running speed for the first 9 miles.

Answer 1

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

$\frac{9}{x}+\frac{5}{x+4}=2$

solve for x

Multiply by x(x+4) both sides

$9(x+4)+5x=2x(x+4)$

$9x+36+5x=2x^2+8x$

$2x^2-6x-36=0$

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