SOLUTION: On a bus trip Frank is flying from new york to london,which are 3600 miles apart. With the wind current the flight there only takes 6 hours. On the return trip the flight takes 8 h

Question 275331: On a bus trip Frank is flying from new york to london,which are 3600 miles apart. With the wind current the flight there only takes 6 hours. On the return trip the flight takes 8 hours against the wind. Write and solve a system of linear equations to determine the airspeed and the wind speed.
please help me solve this word problem
thank you very much! (in advance)
Found 3 solutions by stanbon, Greenfinch, dabanfield:
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
On a bus trip Frank is flying from new york to london,which are 3600 miles apart.
With the wind current the flight there only takes 6 hours.
time = 6 hrs ; distance = 3600 miles ; rate = 3600/6 = 600 mph
---------------------------------------------
On the return trip the flight takes 8 hours against the wind.
time = 8 hrs ; distance = 3600 miles ; rate = 3600/8 = 450 mph
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Write and solve a system of linear equations to determine the airspeed and the wind speed.
-------------------
p + w = 600
p - w = 450
---
Add to get:
2p = 1050
p = 525 mph (speed of the plane in still air)
-----
Substitute to solve for "w":
525 + w = 600
w = 75 mph (speed of the wind)
===================================
Cheers,
Stan H.
Answer by Greenfinch(383)   (Show Source): You can put this solution on YOUR website!
Basic speed is X, so speed with wind is X + W and against is X - W
3600/(X + W) = 6
3600/(X - W) = 8
3600 = 6(X + W)
3600 = 8(X - W)
6X + 6W = 8X - 8W
2X = 14W
X = 7W
Substituting
3600/ 8W = 6
3600 = 48W
W = 75
X = 525
With wind, speed is 600 which takes 6 hours for 3600 miles
Against wind speed is 450 which takes 8 hours for 3600 miles

Answer by dabanfield(803)   (Show Source): You can put this solution on YOUR website!
On a bus trip Frank is flying from new york to london,which are 3600 miles apart. With the wind current the flight there only takes 6 hours. On the return trip the flight takes 8 hours against the wind. Write and solve a system of linear equations to determine the airspeed and the wind speed.
please help me solve this word problem
thank you very much! (in advance)
Remember that distance = rate* time.
Let w be the wind speed and x the air speed. With the wind we have:
1.) 3600 = (x+w)*6
Against the wind we have:
2.) 3600 = (x-w)*8

If we multiply both sides of equation 1.) by 1/6 and both sides of equation 2.) by 1/8 we then have:
3.) 600 = x + w
4.) 450 = x - w
Adding these two equations we have:
1050 = 2x
x = 525
Substituting 525 for x in 3.) above we have:
600 = 525 + w
w = 75

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