Help needed

Question

Part 1

A plane can travel 960 miles in 2 hours with a tail wind. The return trip takes 2 hours and 40 minutes against the wind(use a mixed number or improper fraction to represent time). Find the speed of the plane in still air and the wind speed. Write a system of 2 equations to represent the problem.Don't forget to assign your variables. Do not solve or simplify this question.

Part 2

Use the equation you came up with in Part 1 to solve this system algebraically(using substitution or elimination) Show all work. Find the value for both variables and be sure to interpret the meaning of the values.

Answer 1

Hi, Mya,

Question:  What is the speed of the plane in still air and the wind speed?

  

Start by setting up a table:    Formula    D=Rate* Time     D=distance     Rate= speed of plane in still air

                                                                                                               (Air doesn't  against the plane.)

Let R= Speed of plane in still air

Let X=speed of wind

                                                                                 D              =         R          *        T

Plane has air pushing in the same direction of its

flight.  Air 's force increases speed of plane.                960 mi                R+X             2 hours

 

Plane's return trip-Plane's force forward is being          960 mi                R-X           2 h 40min (2 2/3  h=8/3 hours)

impeded by wind's for pushing the plane back.

Plane's speed is decreased because of wind's action.

 

Note: The plane travels the same distance going and returning flights.

 

960= 2(R+X)

960=8/3 (R-X)

 

Part 2   Use substitution or elimination to solve.   

960=2(R+X)         Simplify by dividing both sides of equation by 2.   960/2  =2/2 (R+X)

  480=R+X         Next, simplify the second equation.

960= (8/3)(R-X)      Multiply both sides of the equation by reciprocal of 8/3.  3/8 (960)= (3/8)(8/3) (R-X)

360= R-X           Now, bring equations together into a system of equations.

 

480=R+X    

360=R-X                  Add two equations together.

 

840=2R                     Divide both sides by number next to R.                   840/2=R       420=R

 

I will let you finish the problem.  Just substitute the value of 420 for "R" into one of the equations to find "X."

If I have helped you, please give me a thumbs up.

                                          Susan C.

 

 

 

 

Answer 2

Hi Mya,

 

Part 1

What you want is to do is represent the speed of the plane and the wind with variables, call them x and y respectively:

x: speed of plane, y: wind speed

x +y =960/2=480  Note: here you  add because you have a tail i.e same direction as the plane.

For the return trip the plane flies against the wind, subtract the y from x, you need to convert the minutes to hours

2hrs 40 min = 2hrs + 40/60 = 2+ 2/3 =(2*3+2)/3 =8/3hrs   (convert to improper fraction)

x-y=960/8/3 = 960*3/8 =120*3 =360

The system of equations are

x + y = 480

x  - y = 360

Part 2

 

x + y = 480

x  - y = 360   this gives x = 360 +y plug into the first equation

 

360 + y  + y = 480

 2y = 120 

y = 60

x = 360 +y = 360 + 60 =420

The plane travels at 420mph and wind speed is 60mph

Answer 3

Hi May,

 

This is a distance rate time problem.

 

For the plane, we have

t_p = 2 hours

r_p = r+w, where r is the speed of the plane and w is the tail wind

d_p = 960 miles

 

For the return trip, we have

t_r = 2 hours 40 minutes = 2.667 hours
r_r = r-w, where r is the speed of the plane and w is the tail wind
d_r = 960 miles

 

d = rt

and 

d_p = d_r = d

 

960 = 2(r+w)

960 = 2.667(r-w)

 

Distributing the coefficient, your system of equations is

 

2r + 2w = 960

2.667r - 2.667w = 960

 

For Part b, let's use substitution.

 

working with the first equation, 

2r + 2w = 960

dividing by 2

r+w = 480

and 

r = 480-w

 

We can substitute this in the 2nd equation.

2.667(480-w) - 2.667w = 960

1280 - 2.667w - 2.667w = 960

 

Combining like term

1280 - 5.333w = 960

320 = 5.333w

60=w

and since r = 480-w

r = 480-60

r = 420

 

So the speed of the plane is 420 mph and the speed of the wind is 60 mph.