SOLUTION: The speed of a plane is 120 miles/hour in a calm. With the wind it can cover a certain distance in 4 hours, but against the wind it can cover only 3/5 of that distance in the same
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Question 414401: The speed of a plane is 120 miles/hour in a calm. With the wind it can cover a certain distance in 4 hours, but against the wind it can cover only 3/5 of that distance in the same time. Find the velocity of the wind.
Here is what I got.
Let X = velocity of the wind in X miles/1 hour.
Calm:
v = 120 miles/1 hour
Downstream:
X miles in 4 hours, or X miles/4 hours, which is 0.25 X miles in 1 hour
Upstream:
3/5 X miles in 4 hours, or 3/20 X miles in 1 hour
Then,
time downstream = time upstream
distance traveled downstream / (velocity of the plane downstream + velocity of the wind) = distance traveled upstream / (velocity of the plane upstream - velocity of the wind)
0.25X miles / [{(120+X) miles}/1 hour] = 3/5X miles / [{(120-X) miles}/1 hour]
0.25X/(120+X) = 0.6X/(120-X)
0.25X (120-X) = (120+X)0.6X
Now I am stuck because I am getting X squarred. Please help. Thank you very much.
Ivana Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! The speed of a plane is 120 miles/hour in a calm.
With the wind it can cover a certain distance in 4 hours, but against the wind
it can cover only 3/5 of that distance in the same time.
Find the velocity of the wind.
:
I think you are making this more complicated than it is:
Let x = velocity of the wind
then
(120+x) = effective speed with the wind
and
(120+x) = effective speed against the wind
:
Change 3/5 to .6
:
Write a distance equation; dist = time * speed
:
"against" dist = .6 times "with" distance
4(120-x) = .6(4(120+x)
480 - 4x = .6(480+ 4x)
480 - 4x = 288 + 2.4x
480 - 288 = 2.4x + 4x
192 = 6.4x
x =
x = 30 mph is velocity of the wind
:
:
Check this by finding the actual distance for each trip
4(120+30) = 600 mi
4(120-30) = 360 mi
Find the fraction that 360/600 = .6 which we would expect if we did this right
