Question

Jean runs 6 mi and then rides 24 mi on her bicycle in a biathlon. She rides 7 mph faster than she rns. If the total time for her to complete the race is 2.25 hr, deterimine her average speed running and her average speed riding her bicycle

Answer 1

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:

$2.25 = \frac{6}{x} +\frac{24}{x+7} =\frac{6(x+7)+24x}{(x)(x+7)} =\frac{6x+42+24x}{x (x+7)} \\2.25=\frac{30x+42}{(x)(x+7)} \\2.25x(x+7)=30x +42\\2.25x^2+15.75x=30x+42\\2.25x^2-14.25x-42= 0$

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