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
by 8:00 a.m., the snack bar had made $3,256 in sales. By noon, the snack bar's total sales were $8,821. On average how much mone
sammy [17]

Answer:

$1,391.25

Step-by-step explanation:

Noon would be 12:00 PM which would be 4 hours ahead of 8:00 AM

We subtract $8,821 by $3,256 to get the amount earned between 8:00 AM and 12:00 PM

$8,821 - $3,256

= $5,565

The find the average taken in within those 4 hours we will have to divide the money earned by the hours

$5,565/4

= $1,391.25

7 0
3 years ago
How do you solve this ? what do you do with the exponets ?
antiseptic1488 [7]
4/7 is the answer. 

I cant reall explain becuase it will take forever xD
6 0
3 years ago
Read 2 more answers
HELP PLEASEE 12 points !!
olga55 [171]

Answer:

Negative since the line is coming like this \

It gets to be negavite will if it was like this/ it could have been positive

7 0
3 years ago
Read 2 more answers
A line passes through the point (4, -6) and has a slope of 3/2 . Write an equation in slope-intercept form for this line.
tatyana61 [14]

A slope intercept form: y = mx + b where m = slope and b = y -intercept

A slope of 3/2 is given

So y = 3/2 x + b

To find b:

b = y - mx

A line passes through the point (4, -6)

b = -6 - (3/2)(4)

b = -6 - 6

b = - 12

Answer

Equation in  slope intercept form:  y = 3/2 x - 12


8 0
3 years ago
Read 2 more answers
Please help me. look at the picture.
Butoxors [25]
It’s 0.775x +2.5 =correct
6 0
2 years ago
Other questions:
  • Which year had an upward trend between month 3 and month 4? this year or last year?
    9·1 answer
  • HELP!!!! 15 points and marked brainliest!!!!
    8·1 answer
  • Factor completely.<br> 18x10-2
    8·1 answer
  • The Cute Kitten Shelter has $486$ cute kittens at the start of Monday. On each day, $\frac13$ of the kittens available at the st
    9·2 answers
  • In the circle, m BC = 94°. The diagram is not drawn to scale.
    12·1 answer
  • For the AAS theorem to apply which side of the triangle must be known?
    10·1 answer
  • Write the value of b when the expression 14.1x + b is<br> equivalent to 4.7(3x – 5).
    8·1 answer
  • 60 children were asked to chose their favourite vegetable from 5 options. Work out the number of children who chose each vegetab
    10·1 answer
  • Please help.. honestly, i just need part a answered!
    14·2 answers
  • Find sec 0<br><br>is my answer correct? if not what's the right answer ​
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!