Question

Tonya ran 15.2 miles in a park as she headed up the hill toward home her speed decrease by 2 mph and she ran 12 miles home at that speed if her total time for the run was three hours 54 minutes find her rate in the park and on the hill

Answer 1

Let x mph be its speed over the park, then x-2 mph is its speed over the hill. In total she ran 15.2 miles through the park and 12 miles up the hill in 3 hours 54 minutes(3,9 hours)

Let's make an equation

$\frac{15,2}{x} +\frac{12}{x-2} =3,9\\15,2(x-2)+12x=3,9x(x-2)\\15,2x-30,4+12x=3,9x^2-7,8x\\3,9x^2-35x+30,4=0\\39x^2-350+304=0\\D=(-350)^2-4*39*304=75076=274^2\\\\x_1=\frac{350+274}{2*39} =8\\\\x_2=\frac{350-274}{2*39} =\frac{12}{13}$

x₂ is not suitable for us, because otherwise the speed on the hill will be negative, and this can not be

Her speed in the park is 8 mph, so her speed on the hill is 8-2=6 mph

Answer: her speed in the park is 8 mph and her speed on the hill is 6 mph.

P.S. Hello from russia :^)