Answer:
Option (5)
Step-by-step explanation:
Lina's speed during the first part of the trip = s miles per hour
If she travels initial 80 miles on this trip with this speed, time taken to cover the distance [tex]t_1=\frac{\text{Distance}}{\text{Speed}}=\frac{80}{s}[/tex] hours
Now speed at which she traveled remaining 50 miles = (s + 10) miles per hour
So the time spent to cover this distance [tex]t_2=\frac{50}{s+10}[/tex] hours
Total time for the complete trip = [tex]t_1+t_2[/tex] = [tex]\frac{80}{s}+\frac{50}{s+10}[/tex]
= [tex]\frac{80(s+10)+50s}{s(s+10)}[/tex]
= [tex]\frac{80s+800+50s}{s(s+10)}[/tex]
= [tex]\frac{130s+800}{s(s+10)}[/tex]
Therefore, Option (5) will be the answer.
Option C is correct. The expressions that represent the total time of her trip in hours is [tex]t_1 + t_2 = \frac{80}{s} +\frac{50}{s+10} \\[/tex]
Let the speed travelled during the first part of the trip be "s"
The formula for calculating the distance is expressed as:
[tex]distance=speed\times time[/tex]
For the first part of the journey:
distance = 80miles
time = t₁
Speed = s
Substitute the given parameters into the formula:
[tex]80 = st_1\\t_1=\frac{80}{s}[/tex]........................................... 1
For the second part of the trip;
Distance travelled = 5 miles
speed = s + 10 (10miles/hour faster than the first part of the trip)
time = t₂
Get the time t₂
[tex]50=(s+10)t_2\\t_2=\frac{50}{s+10}[/tex]
Adding both times taken to get the total time of her trip in hours.
[tex]t_1 + t_2 = \frac{80}{s} +\frac{50}{s+10} \\[/tex]
Hence the expression that represent the total time of her trip in hours is [tex]t_1 + t_2 = \frac{80}{s} +\frac{50}{s+10} \\[/tex]
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