Respuesta :
Answer:
240 mi
Step-by-step explanation:
Felicia spent her 12 hours from home by driving 7 hours and spending 5 hours on Capri. Her speeds were in the ratio 80:60, so her times were in the inverse ratio — 60:80 = 3:4. Since her total time was 7 hours = 3+4 ratio units, each ratio unit must represent 1 hour.
Felicia spent 3 hours driving 80 mph from Rome to Sorrento, and 4 hours driving 60 mph home. The trip each way was ...
... (3 h)×(80 mi/h) = 240 mi = (4 h)×(60 mi/h)
It is 240 miles from Rome to Sorrento.
The distance between Rome and Sorrento is [tex]\boxed{240{\text{}}{\kern 1pt}{\text{miles}}.}[/tex].
Further explanation:
The formula for speed is given as,
[tex]\boxed{s=\frac{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{\kern 1pt} {\text{m/h}}[/tex].
Felicia left from Sorrento to Rome at average speed of [tex]60{\kern 1pt} {\text{m/h}}[/tex].
The total time taken is [tex]12{\kern 1pt} {\text{hours}}[/tex].
Calculation:
Consider distance between Rome to Sorrento as [tex]x{\kern 1pt} {\text{miles}}[/tex].
Felicia returned home after 12 hours. She then took the boat to Capri and return Sorrento 5 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]{t_1}=\dfrac{x}{{80}}[/tex]
The time taken to reach Rome from Sorrento can be calculated as,
[tex]{t_2}=\dfrac{x}{{60}}[/tex]
The total time t 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{\kern 1pt} {\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 aboutbinomial and trinomialhttps://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, returning, averaged, 60 mph.
