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?
 This is what i did

P=Plane Speed
W=Wind Speed

P-W= 780 <---- Miles
P+W=120 <----Comes from the 2 hours....60x2
I added them together and got
2P = 900 then I divided
P=450 MPH

Then I put it in place with P+W=120

450+W=120
W= -330 MPH

Answer 1

Hi Danny,

 

You're confusing wind speed and distance and time.

 

Remember that distance = speed x time

 

The distance is the same flying against the wind as flying with the wind.

 

With the wind--> 780 = rate x 3  so the speed = 780/3 = 260 mph

Against the wind--> 780 = rate x 2 so the speed = 780/2 = 390 mph

 

Now let P = plane speed with no wind  and let W = wind speed

 

P + W = 390

 

P - W = 260

---------------

2P = 650 after adding the two equations

 

P = 325 mph

 

W = 65 mph

 

Dan