Respuesta :
Answer:
Speed during first part of the trip = 50 miles/hour
Speed during second part of trip = 53 miles/hour
Step-by-step explanation:
Given:
Distance driven in rainstorm = 250 miles
Distance driven after rain stopped = 159 miles
Speed driven after rain stopped is 3 miles faster than the speed driven in rainstorm.
Total time driven = 8 hours
To find the speed of the car at each part of the trip.
Solution:
There are two parts of the trip.
1) Car driven in rainstorm:
Let the speed of the car during this part in miles/hour be = [tex]x[/tex]
Distance covered in this part = 250 miles.
Time taken in this trip = [tex]\frac{Distance}{Speed}=\frac{250\ miles}{x\ miles/hour}=\frac{250}{x}\ hours[/tex]
2) Car driven after rain stopped:
Speed of the car during this part in miles/hour will be = [tex]x+3[/tex]
Distance covered in this part = 159 miles.
Time taken in this trip = [tex]\frac{Distance}{Speed}=\frac{159\ miles}{(x+3)\ miles/hour}=\frac{159}{x+3}\ hours[/tex]
Total time driven can be given as:
[tex]\frac{250}{x} +\frac{159}{x+3} = 8[/tex]
Solving for [tex]x[/tex].
Taking LCD.
[tex]\frac{250(x+3)}{x(x+3)}+\frac{159x}{x(x+3)}=8[/tex]
Simplifying.
[tex]\frac{250x+750+159x}{x^2+3x}=8[/tex]
[tex]\frac{409x+750}{x^2+3x}=8[/tex]
Multiplying both sides by [tex](x^2+3x)[/tex]
[tex](x^2+3x)\frac{409x+750}{x^2+3x}=8(x^2+3x)[/tex]
[tex]409x+750=8x^2+24x[/tex]
Subtracting both sides by 750.
[tex]409x+750-750=8x^2+24x-750[/tex]
[tex]409x=8x^2+24x-750[/tex]
Subtracting both sides by [tex]409x[/tex]
[tex]409x-409x=8x^2+24x-409x-750[/tex]
[tex]0=8x^2-385x-750[/tex]
Applying quadratic formula.
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
[tex]x=\frac{-(-385)\pm\sqrt{(-385)^2-4(8)(-750)}}{2(8)}[/tex]
[tex]x=\frac{385\pm415}{16}[/tex]
[tex]x=\frac{385+415}{16}[/tex] and [tex]x=\frac{385-415}{16}[/tex]
∴ [tex]x=50[/tex] and [tex]x=-1.875[/tex]
Since speed cannot be taken as negative, so our solution will be 50 miles per hour.
Speed during first part of the trip = 50 miles/hour
Speed during second part of trip = [tex]50+3[/tex] = 53 miles/hour
