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A girl starts to walk to her school, which is 20 miles away, at 6:50 and at a rate of 3 miles per hour. After a while, her dad p

Alexeev081 [22]

The girl walked a distance of $\boxed{{\mathbf{5 miles}}}$ in her way.

Further explanation:

The time can be calculated as,

${\text{ time}}=\frac{{{\text{distance}}}}{{{\text{speed}}}}$

Given:

It is given that a girl stands 20 miles away from the school at $6:50{\text{ am}}$ and she started walking at the rate of $3{\text{ mi/hr}}$ and then after some time her dad pick up and he drives at the rate of $30{\text{ mi/hr}}$ . They reach the school at $9:00{\text{ am}}$ .

Step by step explanation:

Step 1:

Consider $x$ as the distance she walked in her way.

The speed of the girl when she walked is $3{\text{ mi/hr}}$ .

Now use the formula of time to obtain the walk time.

$\begin{gathered}{\text{ walktime}}=\frac{{{\text{distance walked}}}}{{{\text{walking speed}}}}\hfill\\{\text{ walktime}}=\frac{x}{3}\hfill\\\end{gathered}$

Since the total distance is $20{\text{ miles}}$ .

Then consider $20-x$ as the distance driven by the car.

The driving speed is $30{\text{ mi/hr}}$ .

Now use the formula of time to obtain the drive time.

$\begin{gathered}{\text{drive time}}=\frac{{{\text{distance travelled by car }}}}{{{\text{ speed of car}}}}\hfill\\{\text{drive time}}=\frac{{20-x}}{{30}} \hfill\\\end{gathered}$

Step 2:

Now we calculate the total time took by girl to reach the school.

$9:00-6:50={\text{2 hrs 10 min}}$

Now convert the timing into hours as,

$\begin{aligned}2{\text{ hours 10 minutes}}&=2+\frac{{10}}{{60}}\\&=2\frac{1}{6}\\&=\frac{{13}}{6}{\text{ hrs}}\\\end{aligned}$

Step 3:

Total time is the sum of drive time and walk time.

The total time can be expressed as,

$\frac{x}{3}+\frac{{20-x}}{{30}}=\frac{{13}}{6}$

Now solve the above equation by cross multiply method.

$\begin{aligned}\frac{x}{3}+\frac{{20-x}}{{30}}&=\frac{{13}}{6}\hfill\\\frac{{10x+20-x}}{{30}}&=\frac{{13}}{6}\hfill\\\frac{{9x+20}}{{30}}&=\frac{{13}}{6}\hfill\\6\left({9x+20}\right)&=13\left({30}\right)\hfill\\\end{aligned}$

Now simplify the further equation.

$\begin{aligned}6\left({9x+20}\right)&=13\left({30}\right)\hfill\\54x+120&=390\hfill\\54x&=390-120\hfill\\54x&=270\hfill\\\end{aligned}$

Simplify the further equation.

$\begin{aligned}54x&=270\hfill\\x&=\frac{{270}}{{54}}\hfill\\x&=\frac{{45}}{9}\hfill\\x&=5\hfill\\\end{gathered}$

Therefore, the girl walked 5 miles.

Learn more:

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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

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