airplane and wind rate

Question

flying against the wind, an airplane travels 2190km in 3 hours. Flying with the wind, the same plane travels 8330 km in 7 hours. What is the rate of the plane in still air and what is the rate of the wind?

Answer 1

Use speed*time = distance

 

v = airplane speed in still air

w = wind speed

 

Against the wind:

 

(v-w)(3 hrs) = 2190 km ⇒ v-w = 2190/3 = 730

 

With the wind:

 

(v+w)(7 hrs) = 8330 km ⇒ v+w = 8330/7 = 1190

 

Solve a system of two equations in two unknowns:

 

v - w = 730

v + w = 1190

 

Add the two equations to get v:

 

2v = 1190 + 730 = 1920 ⇒ v = 1920/2 = 960 km/hour

 

Substitute this value of v into either equation, e.g. the top equation:

 

v - w = 960 - w = 730 ⇒ w = 960 - 730 = 230

 

Test the answers:

 

(v-w)(3 hours) = (960 - 230) km/hour * (3 hours) = 2190 km (good)

(v+w)(7 hours) =(960+230) km/hour * (7 hours) = 8330 km (good)

 

Final answer:

 

v = 960 km/hour

w = 230 km/hour (This is an exceptionally high wind speed, but it is consistent with the given information.)