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
[tex]\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}[/tex]
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 :^)
