Answer:
Average running speed: 8.52 mph
Average biking speed: 15.52 mph
Step-by-step explanation:
The formula for velocity is v= d/t where d is distance and t is time.
We know that Jean runs a distance of 6 miles and rides a distance of 24 miles.
We know that if she runs at a x mph, then she rides at x + 7 mph.
From the formula of distance, we get that t = d/v
Therefore, substituting these values in the formula for time we get:
[tex]2.25 = \frac{6}{x} +\frac{24}{x+7} =\frac{6(x+7)+24x}{(x)(x+7)} =\frac{6x+42+24x}{x (x+7)} \\2.25=\frac{30x+42}{(x)(x+7)} \\2.25x(x+7)=30x +42\\2.25x^2+15.75x=30x+42\\2.25x^2-14.25x-42= 0\\[/tex]
If we apply the general formula to this quadratic equation we get:
x= -2.19
x=8.52
Jean cannot have an average negative running speed. Therefore our answer is x= 8.52
And her average running speed is 8.52 mph and her average speed riding her bicycle is 15.52 mph
