Algebra Word Problem

Question

It took 3 hours for a plane, flying against the wind, to travel 780 miles. Flying with the wind on the return trip, it only took 2 hours. What would the speed of the plane have been in still air (no wind)? What was the speed of the wind?

 

Please do this in Linear System Form

Please also leave your explanation thanks....Please I need this for Monday.

Answer 1

Hi Danny,

 

Suppose the speed of the wind is u and that of the plane in still air is v, the need speeds for the trip and return trip respectively are

 

v  - u =780/3 = 260 mph            Note v > u for the plane to move during the first leg of the trip

v + u = 780/2= 390 mph            For the return trip 

Add the two equation to eliminate u

 

2v = 650 mph giving v =325mph 

Pick one of the two equation above and plug in v=325

 

v + u = 390

325 + u = 390, u = 390 - 325 = 65 mph

 

The speed of the plane in still air is 325mph and the speed of the wind is 65mph.