word problem

Question

a pilot can fly a plane 2080 miles with the wind in the same time as she can fly 1920 miles against the wind. If the speed of the wind is 20 mph what is the speed of the airplane in still air 

Answer 1

Speed = Distance / Time.

 

Hence,

Time = Distance / Speed.

OR

Time = Total Distance / Effective Speed.

 

Let's say the speed of plane in still lair is 'x'.

 

Scenario 1 - with the wind - 

Time = total distance / effective speed

Time = 2080 / (x + 20 ).

 

Scenario 2 - against the wind -
Time = total distance / effective speed
Time = 1920 / (x - 20 ).

 

• Both the times are the same !

 

2080 / (x+20) = 1920 / (x-20)

 

2080 * (x-20) = 1920 * (x+20)

 

2080x - 41600 = 1920x + 38400

 

2080x - 1920x = 38400 + 41600

 

160x = 80000

 

x = 500

 

Speed of plane in still air is 500 MPH.

Answer 2

2080=(r+w)t

1920=(r-w)t

2080=(r+20)t

1920=(r-20)t

2080/(r+20)=1920/(r-20)

cross multiply

2080(r-20)=1920(r+20)

1920r+38,400=2080r-41,600

38,400+41,600=2080r-1920r

80,000=160r

r=80,000/160

r=500 mph