SOLUTION: While traveling with the wind a plane flies 300 miles in 40 minutes. It returns against the wind in 45 minutes. Find the air speed of the plane and the rate of the wind. Use a syst

Click here to see ALL problems on Travel Word Problems

Question 6491: While traveling with the wind a plane flies 300 miles in 40 minutes. It returns against the wind in 45 minutes. Find the air speed of the plane and the rate of the wind. Use a system of equations to solve the problem
Answer by srinivas123(23) (Show Source):
You can put this solution on YOUR website!
While traveling with the wind a plane flies 300 miles in 40 minutes. It returns against the wind in 45 minutes. Find the air speed of the plane and the rate of the wind. Use a system of equations to solve the problem

Let the speed of plane be X
Let the speed of air be Y
Total distance covered = 300miles .
while going along the wind the speeds add.
Total speed of plane is X+Y
Time taken = 40 mins or 2/3 hour.
time = distance/speed.
so 2/3 = 300 /(x+y)
----> 2(X+Y)=3*300
----> 2(X+Y)=900
----> X+Y = 450 equation (1).
While going against the wind the speeds are subtracted since wind is opposing you.
Time taken to return = 45mins ---->3/4 hour.
Distance = 300 miles .
Time = distance/speed.
So,
3/4 = 300/(X-Y)
----> 3(X-Y)=4*300
----> X-Y = 1200/3 ----> X-Y = 400 equation (2).

adding equation (1) and (2) we get
X+Y=450
(+) X-Y=400
2X=850 ----> X=425 miles / hour.
Substituting this value in Equation (1) we get Y=25 miles/hour .
Hence speed of plane is 425 miles/hour and speed of air is 25 miles/hour