SOLUTION: Fern can fly her plane 240 miles against the wind in the same time it takes her to fly 360 miles with the wind. The speed of the plane in still air is 30 mph more than 4 times the

Question 606328: Fern can fly her plane 240 miles against the wind in the same time it takes her to fly 360 miles with the wind. The speed of the plane in still air is 30 mph more than 4 times the speed of the wind. Find the speed of the plane in still air.
Answer by htmentor(1343) (Show Source): You can put this solution on YOUR website!
Fern can fly her plane 240 miles against the wind in the same time it takes her to fly 360 miles with the wind. The speed of the plane in still air is 30 mph more than 4 times the speed of the wind. Find the speed of the plane in still air.
=========================
Let v = the speed in still air
Let w = the speed of the wind
The speed with the wind is v + w, the speed against the wind is v - w
Given: v = 4w + 30 [speed in still air is 30 more than 4 times the wind speed]
Solve for w:
w = (v-30)/4
Since time = distance/speed, and the times are the same, we can write
240/(v-w) = 360/(v+w)
Using the expression for w above, we have
240/(v-(v-30)/4) = 360/(v+(v-30)/4)
Simplifying and solving for v gives v = 150 mph
Check: w = (150-30)/4 = 30 mph
240/(150-30) = 360/(150+30)
240/120 = 2
360/180 = 2
RELATED QUESTIONS
In the time it takes a pilot to fly 360 miles with a head wind, she can only fly 240... (answered by robertb)

Lauren can fly her plane 180 miles against the wind in the same time it takes him to fly... (answered by Alan3354)

In the time it takes to fliy 360 miles with a head wind, she can only fly 240 mies... (answered by ankor@dixie-net.com)

A small plane can fly 180 miles against a 30 mph wind in the same amount of time it takes (answered by josmiceli)

A plane can travel 640 miles against the wind in the same time it can travel 800 miles... (answered by nerdybill)

An airplane can fly 90 miles against the wind in the same time it takes to fly 110 miles... (answered by fractalier)

A light private plane can fly 120 mph in still air. Flying against the wind, the plane... (answered by checkley77)

Erica flys her plane 200 mi against the wind in the same time it takes her to fly 300 mi... (answered by jorel1380)

A plane can fly 36 miles with the wind, in the same amount of time that it can fly 12... (answered by askmemath)