Respuesta :
Answer:
490 miles.
Step-by-step explanation:
We can see that Felicia returned home after 12 hours. We will subtract 5 from 12 to find number of hours she spent in going from Rome to Sorrento and returning from Sorrento to Rome.
[tex]12-5=7[/tex]
Felicia took 7 hours in her trip from Rome to Sorrento and Sorrento to Rome.
We will use [tex]\text{Distance}=\text{ Speed}*\text{ Time}[/tex] formula to find distance Felicia traveled in 7 hours.
[tex]\text{Distance traveled by Felicia}=7*(80+60)[/tex]
[tex]\text{Distance traveled by Felicia}=7*(140)[/tex]
[tex]\text{Distance traveled by Felicia}=980[/tex]
Now we will divide our total distance by 2 to find distance between Rome and Sorrento.
[tex]\text{Distance between Rome and Sorrento}=\frac{980}{2}[/tex]
[tex]\text{Distance between Rome and Sorrento}=490[/tex]
Therefore, distance between Rome and Sorrento is 490 miles.
The distance between Rome and Sorrento is [tex]\boxed{240\,{\text{miles}}}[/tex].
Further Explanation:
The formula for speed is given as,
[tex]\boxed{s = \dfrac{d}{t}}[/tex]
Here, [tex]s[/tex] represents the speed, [tex]d[/tex] represents the distance, and [tex]t[/tex] represents time.
Given:
Felicia left from Rome to Sorrento at average speed of [tex]80\,{\text{m/h}}[/tex].
Felicia left from Sorrento to Rome at average speed of [tex]60\,{\text{m/h}}[/tex].
The total time taken is [tex]12\,{\text{hours}}[/tex].
Calculation:
Consider distance between Rome to Sorrento as [tex]x\,{\text{miles}}[/tex].
Felicia returned home after [tex]12[/tex] hours. She then took the boat to Capri and return Sorrento [tex]5[/tex] hours later.
Therefore, the time t she spent in going from Rome to Sorrento and Sorrento to Rome can be calculated as,
[tex]\begin{aligned}{\text{Time}} &= 12 - 5 \\ &= 7 \\ \end{aligned}[/tex]
The formula for time can be expressed as,
[tex]\boxed{{\text{Time}} = \dfrac{{{\text{distance}}}}{{{\text{speed}}}}}[/tex]
The time taken to reach Sorrento from Rome can be calculated as,
[tex]\boxed{{t_1} = \frac{x}{{80}}}[/tex]
The time taken to reach Rome from Sorrento can be calculated as,
[tex]\boxed{{t_2} = \dfrac{x}{{60}}}[/tex]
The total time [tex]t[/tex] is the sum of [tex]{t_1}[/tex] and [tex]{t_2}[/tex].
[tex]\begin{aligned}7 &= \frac{x}{{80}} + \frac{x}{{60}} \\ 7 &= \frac{{60x + 80x}}{{80 \times 60}} \\ 7 &= \frac{{140x}}{{4800}} \\ 7 \times \frac{{4800}}{{140}} &= x \\ 240 &= x \\ \end{aligned}[/tex]
The distance between Rome and Sorrento is [tex]\boxed{240\,{\text{miles}}}[/tex].
Learn more:
1. Learn more about unit conversion https://brainly.com/question/4837736
2. Learn more about non-collinear https://brainly.com/question/4165000
3. Learn more about binomial and trinomial https://brainly.com/question/1394854
Answer details:
Grade: High School
Subject: Mathematics
Chapter: Linear equation
Keywords: Felicia, home, Ferrari, Rome, Sorrento, average, returning, Capri, boat, average speed, far, distance, speed, time.
