Respuesta :
The girl walked a distance of [tex]\boxed{{\mathbf{5 miles}}}[/tex] in her way.
Further explanation:
The time can be calculated as,
[tex]{\text{ time}}=\frac{{{\text{distance}}}}{{{\text{speed}}}}[/tex]
Given:
It is given that a girl stands 20 miles away from the school at [tex]6:50{\text{ am}}[/tex] and she started walking at the rate of [tex]3{\text{ mi/hr}}[/tex] and then after some time her dad pick up and he drives at the rate of [tex]30{\text{ mi/hr}}[/tex] . They reach the school at [tex]9:00{\text{ am}}[/tex] .
Step by step explanation:
Step 1:
Consider [tex]x[/tex] as the distance she walked in her way.
The speed of the girl when she walked is [tex]3{\text{ mi/hr}}[/tex] .
Now use the formula of time to obtain the walk time.
[tex]\begin{gathered}{\text{ walktime}}=\frac{{{\text{distance walked}}}}{{{\text{walking speed}}}}\hfill\\{\text{ walktime}}=\frac{x}{3}\hfill\\\end{gathered}[/tex]
Since the total distance is [tex]20{\text{ miles}}[/tex] .
Then consider [tex]20-x[/tex] as the distance driven by the car.
The driving speed is [tex]30{\text{ mi/hr}}[/tex] .
Now use the formula of time to obtain the drive time.
[tex]\begin{gathered}{\text{drive time}}=\frac{{{\text{distance travelled by car }}}}{{{\text{ speed of car}}}}\hfill\\{\text{drive time}}=\frac{{20-x}}{{30}} \hfill\\\end{gathered}[/tex]
Step 2:
Now we calculate the total time took by girl to reach the school.
[tex]9:00-6:50={\text{2 hrs 10 min}}[/tex]
Now convert the timing into hours as,
[tex]\begin{aligned}2{\text{ hours 10 minutes}}&=2+\frac{{10}}{{60}}\\&=2\frac{1}{6}\\&=\frac{{13}}{6}{\text{ hrs}}\\\end{aligned}[/tex]
Step 3:
Total time is the sum of drive time and walk time.
The total time can be expressed as,
[tex]\frac{x}{3}+\frac{{20-x}}{{30}}=\frac{{13}}{6}[/tex]
Now solve the above equation by cross multiply method.
[tex]\begin{aligned}\frac{x}{3}+\frac{{20-x}}{{30}}&=\frac{{13}}{6}\hfill\\\frac{{10x+20-x}}{{30}}&=\frac{{13}}{6}\hfill\\\frac{{9x+20}}{{30}}&=\frac{{13}}{6}\hfill\\6\left({9x+20}\right)&=13\left({30}\right)\hfill\\\end{aligned}[/tex]
Now simplify the further equation.
[tex]\begin{aligned}6\left({9x+20}\right)&=13\left({30}\right)\hfill\\54x+120&=390\hfill\\54x&=390-120\hfill\\54x&=270\hfill\\\end{aligned}[/tex]
Simplify the further equation.
[tex]\begin{aligned}54x&=270\hfill\\x&=\frac{{270}}{{54}}\hfill\\x&=\frac{{45}}{9}\hfill\\x&=5\hfill\\\end{gathered}[/tex]
Therefore, the girl walked 5 miles.
Learn more:
- Learn more about the distance between the points https://brainly.com/question/6278187
- Learn more about the equivalent fraction https://brainly.com/question/952259
- Learn more about midpoint of the segment https://brainly.com/question/3269852
Answer details:
Grade: High school
Subject: Mathematics
Chapter: Speed, distance and time
Keywords: girl, distance, drive, walk, drive time, dad, speed, travelled, formula, cross multiply, fraction, number, multiply, addition, subtraction, equation, school
