Respuesta :
Answer:
The reasonable number of days to reach Indianapolis is 3 days.
Step-by-step explanation:
Total distance to be covered from Houston to Indianapolis, d= 1022 miles.
As they plan to drive between 425 and 475 miles/day, so the range of the rate of driving per day, r, is 425<r<475.
Let t day is the reasonable number of days to complete the journey.
As time = (distance)/(speed), so
[tex]t=\frac d r\cdots(i)[/tex]
The given range of the rate is
[tex]425<r<475[/tex]
If [tex]a>b[/tex], than [tex]1/a<1/b[/tex] for [tex]a,b\neq0[/tex];
[tex]\Rightarrow \frac {1}{425}>\frac {1}{r} >\frac{1}{475}[/tex]
If a>b, the for any [tex]\alpha>0[/tex], [tex]a\alpha>b\alpha[/tex], so multiply the above equation by [tex]d[/tex], we have
[tex]\frac {d}{425}>\frac {d}{r} >\frac{d}{475}[/tex]
[tex]\Rightarrow \frac {d}{425}>t >\frac{d}{475}[/tex] [from equation (i)]
[tex]\Rightarrow \frac {1022}{425}>t >\frac{1022}{475}[/tex] [given, d=1022 miles]
[tex]\Rightarrow \frac {1022}{425}>t >\frac{1022}{475}[/tex]
[tex]\Rightarrow 2.40>t >2.15[/tex]
So, to cover the distance of 1022 miles, with the speed in between 425 miles/day and 475 miles/day, Jerry's family will take in between 2.40 days and 2.15 days. This means, for the given speed range, they need 2 complete days and some fraction of 3rd day to reach Indianapolis.
Hence, the reasonable number of days to reach Indianapolis is 3 days.
