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nordsb [41]
3 years ago
5

Flying against the wind, an airplane travels 4000 kilometers in 5 hours. Flying with the wind, the same plane travels 5040 kilom

eters in 4 hours. What is the rate of the plane in still air and what is the rate of the wind? Urgent!!
Mathematics
1 answer:
andriy [413]3 years ago
7 0

Answer:the plane in still air is 904 km/h

the rate of the wind is 104 km/h

Step-by-step explanation:

Let x represent the rate or speed of the plane in still air.

Let y represent the rate or speed of the wind.

Flying against the wind, an airplane travels 4000 kilometers in 5 hours. This means that the total speed of the airplane would be (x - y) km/h

Distance = speed × time

Therefore

4000 = 5(x - y)

4000 = 5x - 5y - - - - - - - - -1

Flying with the wind, the same plane travels 5040 kilometers in 4 hours. This means that the total speed of the airplane would be (x + y) km/h. Therefore,

5040 = 4(x + y)

5040 = 4x + 4y - - - - - - - - - 2

Multiplying equation 1 by 4 and equation 2 by 5, it becomes

16000 = 20x - 20y

20160 = 20x + 20y

Subtracting, it becomes

- 4160 = - 40y

y = - 4160/-40

y = 104

Substituting y = 104 into equation 1, it becomes

4000 = 5x - 5 × 104

4000 = 5x - 520

5x = 4000 + 520

5x = 4520

x = 4520/5 = 904

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A bag contains white marbles and red marbles, 20 in total. The number of white marbles is 5 more than 2 times the number of red
Nitella [24]

Answer:

15

Step-by-step explanation:

let r represent red marbles then white = 2r + 5 and total is 20, thus

r + 2r + 5 = 20 ( subtract 5 from both sides )

3r = 15 ( divide both sides by 3 )

r = 5 ← number of red marbles

Thus number of white = 20 - 5 = 15

7 0
3 years ago
How many solutions does this linear system have? y =2/3 x+ 2 6x – 4y = –10
ZanzabumX [31]
2.  They are both straight lines.  The solution of a linear system is where the two lines intersect, and if they're both straight lines, then they can only cross once.  

See the picture attached.

8 0
3 years ago
The temperature fell 12°F from 46°Fto 34°F in 10 hours. how much would the temperature fall over 15 hours if the pattern continu
Stolb23 [73]
18 degrees F because 
it dropped 12 degrees=10 hours
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x is what you want to find out which is how many degrees it would drop in 15 hours.
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5 0
3 years ago
1.) -2(6 - 2x) = 4(-3 + x)<br> 2.) 5 - 1(2x + 3) = -2(4 + x)
Scrat [10]

Let's solve your equation step-by-step.

Question 1:   −2(6−2x) =4(−3+x)

 

Step 1: Simplify both sides of the equation.

−2(6−2x) =4(−3+x)

(−2) (6) +(−2) (−2x) =(4)(−3)+(4)(x)(Distribute)

−12+4x=−12+4x

4x−12=4x−12

 

Step 2: Subtract 4x from both sides.

4x−12−4x=4x−12−4x

−12=−12

 

Step 3: Add 12 to both sides.

−12+12=−12+12

0=0

Answer: All real numbers are solutions.

Question 2:  

Let's solve your equation step-by-step.

5−1(2x+3) =−2(4+x)

 

Step 1: Simplify both sides of the equation.

5−1(2x+3) =−2(4+x)

5+(−1) (2x) +(−1) (3) =(−2) (4)+(−2)(x)(Distribute)

5+−2x+−3=−8+−2x

(−2x) +(5+−3) =−2x−8(Combine Like Terms)

−2x+2=−2x−8

−2x+2=−2x−8

 

Step 2: Add 2x to both sides.

−2x+2+2x=−2x−8+2x

2=−8

 

Step 3: Subtract 2 from both sides.

2−2=−8−2

0=−10

 

Answer: There are no solutions.

 

8 0
3 years ago
According to the distributive property, a(5 + b) = A) 5a + b Eliminate B) 5a + ab C) a (b + 5) D) 5 (a + b)
MArishka [77]
A(b+c)=ab+ac
a(5+b)=a(5)+a(b)=5a+ab


B is answer
7 0
3 years ago
Read 2 more answers
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