Help me please

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:

Learn more about the distance between the points brainly.com/question/6278187

Learn more about the equivalent fraction brainly.com/question/952259

Learn more about midpoint of the segment 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

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fiasKO [112]

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yKpoI14uk [10]

Answer:

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Step-by-step explanation:

3/12

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A health club sold ten memberships in one week for total of $3000. If male memberships cost $300 and female memberships cost $30

Ket [755]

Answer:

Step-by-step explanation:

The reason you haven't gotten an answer to this is because in its current formatting, there is no answer. Here's what I mean:

The first equation is going to be concerning the NUMBER of memberships sold, where m is male and f is female. The total number of memberships was 10:

m + f = 10

Now for the money equation. The total amount of money made from that number of memberships was 3000, where male memberships cost $300 and so do the female memberships, giving us an equation of

300m + 300f = 3000

Go back to the first equation and solve for either m or f. I solved for m in terms of f:

m = 10 - f and sub that into the second equation for m to get:

300(10 - f) + 300f = 3000 and

3000 - 300f + 300f = 3000. Here is where you find the problem. The -300f and the 300f cancel each other out, leaving you with the fact that

3000 = 3000 which it does, but it doesn't give us any viable answer.

I would have to say that since we can't do math on this, that the most credible answer you'll find is that the same number of male and female memberships were sold because 5 male memberships cost $1500 (5 memberships at $300 a piece is $1500) and 5 female memberships also cost $1500.

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Step-by-step explanation:

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