1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
notsponge [240]
3 years ago
15

PLEASE HELP A flight across the US takes longer east to west then it does west to east. This is due to the plane having a headwi

nd flying westward (thus slowing it down) and a tailwind flying eastward (thus pushing it along faster). Suppose you are flying from Philadelphia, PA to San Diego, CA. The distance between the cities is 2,400 miles and the plane's speed is 450 mi/hr. What is the speed of the wind?
Complete the chart
Going westward- Distance - Rate- Time
Going Eastward-

Write an equation to represent the total time if the round trip takes 11 hours.

Solve your equation to find the speed of the wind. Round to the nearest mph.
PLEASE HELP!

PLEASE ANSWER CORRECTLY TO GET BRAINLIEST ANSWER
Mathematics
1 answer:
il63 [147K]3 years ago
6 0
To solve our questions, we are going to use the kinematic equation for distance: d=vt
where
d is distance 
v is speed  
t is time 

1. Let v_{w} be the speed of the wind, t_{w} be time of the westward trip, and t_{e} the time of the eastward trip. We know from our problem that the distance between the cities is 2,400 miles, so d=2400. We also know that the speed of the plane is 450 mi/hr, so v=450. Now we can use our equation the relate the unknown quantities with the quantities that we know:

<span>Going westward:
The plane is flying against the wind, so we need to subtract the speed of the wind form the speed of the plane:
</span>d=vt
2400=(450-v_{w})t_{w}

Going eastward:
The plane is flying with the wind, so we need to add the speed of the wind to the speed of the plane:
d=vt
2400=(450+v_{w})t_{e}

We can conclude that you should complete the chart as follows:
Going westward -Distance: 2400 Rate:450-v_w Time:t_w
Going eastward -Distance: 2400 Rate:450+v_w Time:t_e

2. Notice that we already have to equations:
Going westward: 2400=(450-v_{w})t_{w} equation(1)
Going eastward: 2400=(450+v_{w})t_{e} equation (2)

Let t_{t} be the time of the round trip. We know from our problem that the round trip takes 11 hours, so t_{t}=11, but we also know that the time round trip is the time of the westward trip plus the time of the eastward trip, so t_{t}=t_w+t_e. Using this equation we can express t_w in terms of t_e:
t_{t}=t_w+t_e
11=t_w+t_e equation
t_w=11-t_e equation (3)
Now, we can replace equation (3) in equation (1) to create a system of equations with two unknowns: 
2400=(450-v_{w})t_{w}
2400=(450-v_{w})(11-t_e) 

We can conclude that the system of equations that represent the situation if the round trip takes 11 hours is:
2400=(450-v_{w})(11-t_e) equation (1)
2400=(450+v_{w})t_{e} equation (2)

3. Lets solve our system of equations to find the speed of the wind: 
2400=(450-v_{w})(11-t_e) equation (1)
2400=(450+v_{w})t_{e} equation (2)

Step 1. Solve for t_{e} in equation (2)
2400=(450+v_{w})t_{e}
t_{e}= \frac{2400}{450+v_{w}} equation (3)

Step 2. Replace equation (3) in equation (1) and solve for v_w:
2400=(450-v_{w})(11-t_e)
2400=(450-v_{w})(11-\frac{2400}{450+v_{w}} )
2400=(450-v_{w})( \frac{4950+11v_w-2400}{450+v_{w}} )
2400=(450-v_{w})( \frac{255011v_w}{450+v_{w}} )
2400= \frac{1147500+4950v_w-2550v_w-11(v_w)^2}{450+v_{w}}
2400(450+v_{w})=1147500+2400v_w-11(v_w)^2
1080000+2400v_w=1147500+2400v_w-11(v_w)^2
(11v_w)^2-67500=0
11(v_w)^2=67500
(v_w)^2= \frac{67500}{11}
v_w= \sqrt{\frac{67500}{11}}
v_w=78

We can conclude that the speed of the wind is 78 mi/hr.
You might be interested in
‼️‼️ASAP need help ‼️
lozanna [386]
For a shape to be a square all the angles need to be 90 degrees.

Angle B = 3x+60 = 90

3x +60 = 90

Subtract 60 from each side:

3x = 30

Divide both sides by 3:
x = 30 /3
X = 10
5 0
3 years ago
Read 2 more answers
a comedy show sells lower level tickets for $78 and upper level tickets for $59. on the opening knight 2368 tickets were sold fo
shusha [124]
Let L represent lower level tickets and U upper level.

Starter equations:
L + U = 2368
78L + 59U = 157800

Solve simultaneous equations:
59L + 59U = 139712
so 19L = 18088
L = 952
U = 2368 - 952 = 1416

952 lower level tickets and 1416 upper level tickets were sold.
3 0
3 years ago
0.6 of the Chang family expenses are for internet service what fraction of the family's expenses is for internet service put the
sattari [20]
0.6=6/10 so after simplifying you get 3/5, hope it helps !!
4 0
3 years ago
Your gross income is $56k and the standard deduction is $12,200, how much do you owe in taxes?
Neko [114]
8 percent is the answer
5 0
2 years ago
4/9 of the audience at a concert, 1/2 of the remainder are woman and the rest are children. If there are 26 boys and 9 girls, wh
Anna [14]
The amount is 1/7th. Your welcome.
6 0
2 years ago
Read 2 more answers
Other questions:
  • <img src="https://tex.z-dn.net/?f=4%5Csqrt%5Cfrac%7B132%7D%7B143%7D%20%5E%20-2%7D" id="TexFormula1" title="4\sqrt\frac{132}{143}
    13·1 answer
  • Which type of triangle is formed by joining the vertices A(-3, 6), B(2, 1), and ((9,5)?
    15·1 answer
  • Complete the inequalities by
    14·1 answer
  • Is the point (20,13) on this line? Explain your reasoning​
    8·2 answers
  • What is 2x+y=17 in liner equation in slope intercept form?​
    13·1 answer
  • Heeelllllppp meeeeeee
    7·1 answer
  • PLease help! 20 points!!
    6·2 answers
  • Need help solving this puzzle
    15·1 answer
  • How can probabilities be used to make predictions?
    10·2 answers
  • Numerical expressions <br> X + 5=2<br> M - 2 =3<br> X/-8 = -1<br> 5G=-20<br> 1P/6 =0<br> D-15=14
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!