An airplane flies 1764 miles into the wind for 14 hours. The return trip takes 9 hours. Find the speed of the airplane without a wind and the speed of the wind.

Question

I really need help I'm stuck 

Answer 1

Hi Jasmine,

 

The relationship between distance, time, and speed is d/t = s.

 

So the trip into the wind saw the plane travel 1764 miles in 14 hours.  1764 miles/14 hours = 126 miles per hour

The trip with the wind saw the plane travel 1764 miles in 9 hours.  1764 miles/9 hours = 196 miles per hour

 

We can write the following equations using the rate of the plane (P) and the rate of the wind (W)

 

P + W = 196

P - W = 126

 

Adding these equations together

2P = 322

P = 161

 

If P = 161 and P + W = 196,

then 161 + W = 196

W = 35

 

So the planes speed is 161 mph and the wind's speed is 35 mph.

 

Hope this helps!!  :)

Answer 2

v = speed without wind

w = wind speed

 

(v - w)(14 hours) = 1764 miles ⇒ v - w = 1764/14 = 126

(v + w)(9 hours) = 1764 miles ⇒ v + w = 1764/9 = 196

 

Add the 2 equations:

 

2v = 126 + 196 = 322

 

v = 322/2 = 161 mph

 

w = v - 126 = 161 - 126 = 35 mph