Problem

Solve the following problems. $EXpla1n$ how you arrived at your answers.
$1.$ A rectangular garden has an area of $84m^{2}and$ a perimeter of $38m$ Find $nd$ its length and width.
$2.$ A children's park is $350mlon$ long and $200m$ wide. It is surrounded $loy$ a pathway of uniform
width. Suppose the total area of the park and the $pathway$ is $74,464m^{2}.$ $HoM$ wide is the
pathway?
$3.$ A $car$ travels $20$ kph faster than a truck. The car $COVerS$ $350km$ in $twO$ hours less than the
time it takes the truck to travel the same distance. What is the speed of the car? How about
the truck?

7th-9th grade

Algebra

Search count: 105

Solution

Qanda teacher - Ashritha

1.) Let s = the speed of the truck
and (s+20) = the speed of the car
to get the time of each vehicle time = distance/ speed
truck time = 350/s
car time = 350/(s+20)
Truck time - car time = 2 hrs so,
(350/s) - [350/(s+20)] = 2
LCD we can get
[350(s+20) - 350s]/s(s+20) = 2
then transpose the denominator
350(s+20) - 350s = 2s(s+20)
simplifying we can get
350s + 7000 - 350s = 2s^2 + 40s
then simplify more to become quadratic equation
2s^2 + 40s - 7000 = 0
to make it simplest divide the equation by 2
s^2 + 20s - 3500 = 0
by factoring we can get
s= 50
s= -70 (impossible because of the sign)
so
s = 50 km/h is the speed of the truck
s + 20 = 70 km/h is the speed of car

3rd answer is above text

2nd answer in above picture

first we'll get the answer using arithmetic and then using quadratic equations
38/2=19, half of the perimeter
84=2*2*3*7=(2*2*3)*(7)=12*7 and 12+7=19
length and width are 7 and 12 or 12 and 7 (meters)
P=2l+2w
38=2l+2w
19=l+w
l=19-w
A=lw
84=(19-w)w
84=19w-w2
w2-19w+84=0
factor
now, you factor 84 which is what I did at the top...
84=(2*2*3)*(7)
(w-12)(w-7)=0
w-12=0
w=12 (and l=7)
or,...
w-7=0
w=7 (and l=12)

3rd answer in above text

I didn't have notebook with me present so i sent you text answer if you want a written answer you can ask me i will send you later if you want

sorry last text is 1st answer

Student

thank you so much maam.

Qanda teacher - Ashritha

you are welcome

Student

can i know your name on facebook? because I need someone to teach me this is my last coins and I do not know how to get coins

by the way im grade 9 student

Qanda teacher - Ashritha

actually i am really sorry we are not allowed to share our personal information so i can't help you with this

please understand

Student

oh its fine i just need someone to teach me

Qanda teacher - Ashritha

okay thanks for understanding

Student

can you be my tutor only here?

Qanda teacher - Ashritha

yes but i can't answer for the questions here because it in our rules we can't answer here for more questions you have to ask seperately

Student

its ok thank you! ♥️

Qanda teacher - Ashritha

?☺️

please evaluate the answer

Student

hi maam

can i ask something?

is the number I circled like this?

i just need your answer right now

Qanda teacher - Ashritha

i didn't understand?

what?

Student

you send me this answer

1.) Let s = the speed of the truck
and (s+20) = the speed of the car
to get the time of each vehicle time = distance/ speed
truck time = 350/s
car time = 350/(s+20)
Truck time - car time = 2 hrs so,
(350/s) - [350/(s+20)] = 2
LCD we can get
[350(s+20) - 350s]/s(s+20) = 2
then transpose the denominator
350(s+20) - 350s = 2s(s+20)
simplifying we can get
350s + 7000 - 350s = 2s^2 + 40s
then simplify more to become quadratic equation
2s^2 + 40s - 7000 = 0
to make it simplest divide the equation by 2
s^2 + 20s - 3500 = 0
by factoring we can get
s= 50
s= -70 (impossible because of the sign)
so
s = 50 km/h is the speed of the truck
s + 20 = 70 km/h is the speed of car

Qanda teacher - Ashritha

yes what is your doubt in that

Student

is the s^2 is like this? s²

Qanda teacher - Ashritha

yes its s square

Student

ok thank you

Qanda teacher - Ashritha

you are welcome

Student

encircle the correct answer i ask the 7 questions in the other teacher

maam please help me with this

Qanda teacher - Ashritha

Student

thank you so much maam! ❤️

Qanda teacher - Ashritha

you are welcome

please evaluate the answer

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