Question 868456: A plane traveled 300 miles to houston and back. The trip there was with the wind. It took 3 hours. The trip back was into the wind. The trip back took 5 hours. Find the speed of the plane in stil air and the speed of the wind.
Found 2 solutions by mananth, JLJL:
Answer by mananth(16946)   (Show Source):
You can put this solution on YOUR website! Plane speed =x mph
wind speed =y mph
against wind 5 hours
with wind 3 hours
Distance against 300 miles distance with 300 miles
t=d/r against wind -
300.00 / ( x - y )= 5.00
5.00 ( x - y ) = 3.00
5.00 x - 5.00 y = 300.00 ....................1
300.00 / ( x + y )= 3.00
3.00 ( x + y ) = 300.00
3.00 x + 3.00 y = 300.00 ...............2
Multiply (1) by 3.00
Multiply (2) by 5.00
we get
15.00 x + -15.00 y = 900.00
15.00 x + 15.00 y = 1500.00
30.00 x = 2400.00
/ 30.00
x = 80.00 mph
plug value of x in (1) y
5.00 x -5.00 y = 300.00
400.00 -5.00 -400.00 = 300.00
-5.00 y = 300.00
-5.00 y = -100.00 mph
y = 20.00
Plane speed 80.00 mph
wind speed 20.00 mph
m.ananth@hotmail.ca
Answer by JLJL(8)  (Show Source):
You can put this solution on YOUR website! This question involve distance, time and speed. Thus, we have to use the formula, distance = speed x time
Let the speed of the plane be X
Let the speed of the wind be Y
Since total journey takes 300 miles, that means one way trip would be 150 miles.
When flying to Houston, distance = 150 miles. time = 3 hours. The speed of the plane and wind would be X + Y because both are in the same direction. Thus, the first algebraic expression could be established as follow.
distance / speed = time
150/(X + Y) = 3
X + Y = 150/3
X + Y = 50 ------------- (1)
When flying back from Houston, distance = 150 miles. times = 5 hours. The speed of the plane and wind would be X - Y because both are going against each other in direction, thus, one of the speeds would have to be in negative value. Now, we can establish the second algebraic expression as follow.
distance / speed = time
150/(X - Y) = 5
X - Y = 150/5
X - Y = 30 ------------- (2)
Solve equation (1) and (2) simultaneously would give X = 40 and Y = 10
Conclusion: The speed of the plane is 40 miles/hour whereas the speed of the wind is 10 miles/hour.
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