Respuesta :
Jamie spent 30 hours driving to and from her parents house.
Total distance of one trip= 720 miles.
Let x be her speed when she was travelling back home. So her speed on her way to her parents home will be x + 14
Distance = Speed x Time
So,
Time = Distance/Speed
While travelling towards her parents house, the equation for time will be:
Time = [tex] \frac{720}{x+14} [/tex]
While travelling back to her house, the equation for time will be:
Time = [tex] \frac{720}{x} [/tex]
It took her a total of 30 hours, so we can write:
[tex]30= \frac{720}{x}+ \frac{720}{x+14} \\ \\ 30= \frac{720(x+14)+720(x)}{x(x+14)} \\ \\ 30x(x+14)=720x +10080+720x \\ \\ 30 x^{2} + 420x=1440x+10080 \\ \\ 30 x^{2} - 1020x - 10080=0 \\ \\ 30( x^{2} -34x-336)=0 \\ \\ x^{2} -34x-336=0 \\ \\ x^{2} -42x+8x-336=0 \\ \\ x(x-42)+8(x-42)=0 \\ \\ (x-42)(x+8)=0 \\ \\ x=42,x=-8 [/tex]
Since x represents the speed and it cannot have a negative value we ignore x= - 8.
So, Jamie's speed on her way back home was 42 miles per hour. And her speed on her way to her parents home was 42+14 = 56 miles per hour
The time she spent driving towards her parent home = 720/56 = 12 hours and 51 minutes
The time she spent driving towards her home = 720/42 = 17 hours and 9 minutes
Total distance of one trip= 720 miles.
Let x be her speed when she was travelling back home. So her speed on her way to her parents home will be x + 14
Distance = Speed x Time
So,
Time = Distance/Speed
While travelling towards her parents house, the equation for time will be:
Time = [tex] \frac{720}{x+14} [/tex]
While travelling back to her house, the equation for time will be:
Time = [tex] \frac{720}{x} [/tex]
It took her a total of 30 hours, so we can write:
[tex]30= \frac{720}{x}+ \frac{720}{x+14} \\ \\ 30= \frac{720(x+14)+720(x)}{x(x+14)} \\ \\ 30x(x+14)=720x +10080+720x \\ \\ 30 x^{2} + 420x=1440x+10080 \\ \\ 30 x^{2} - 1020x - 10080=0 \\ \\ 30( x^{2} -34x-336)=0 \\ \\ x^{2} -34x-336=0 \\ \\ x^{2} -42x+8x-336=0 \\ \\ x(x-42)+8(x-42)=0 \\ \\ (x-42)(x+8)=0 \\ \\ x=42,x=-8 [/tex]
Since x represents the speed and it cannot have a negative value we ignore x= - 8.
So, Jamie's speed on her way back home was 42 miles per hour. And her speed on her way to her parents home was 42+14 = 56 miles per hour
The time she spent driving towards her parent home = 720/56 = 12 hours and 51 minutes
The time she spent driving towards her home = 720/42 = 17 hours and 9 minutes
