SOLUTION: A small airplane can travel 210 mph in still air. The plane can fly 520 miles with the wind in the same time that it can travel 320 miles against the wind. Find the speed of th

Algebra ->  Equations -> SOLUTION: A small airplane can travel 210 mph in still air. The plane can fly 520 miles with the wind in the same time that it can travel 320 miles against the wind. Find the speed of th      Log On


   

Question 1205974: A small airplane can travel 210 mph in still air. The plane can fly 520 miles with the wind in the same time that it can travel 320 miles against the wind.
Find the speed of the wind.
Found 2 solutions by greenestamps, mananth:
Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


Let x be the speed of the wind. Then the speed of the plane with the wind is 210+x, and the speed against the wind is 210-x.

The times are the same, so the ratio of distances is the same as the ratio of speeds:

520%2F320=%28210%2Bx%29%2F%28210-x%29
320%28210%2BX%29=520%28210-X%29
67200%2B320X=109200-520X
840X=42000
X=50

ANSWER: 50mph

CHECK: 520/320=52/32=13/8
(210+50)/(210-50)=260/160=26/16=13/8

Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
A small airplane can travel 210 mph in still air. The plane can fly 520 miles with the wind in the same time that it can travel 320 miles against the wind.
Find the speed of the wind.
let the speed of wind be x mph
A small airplane can travel 210 mph in still air
Distance traveled = 520 miles
With wind the speed of plane will be (210 +x) mph
With wind time = distance/ speed =520/ (210+x) hours
Against wind the plane will travel (210-x) mph
Against wind the time is 320/(210-x) hours
Time is same to and fro.
520/(210+x) = 320/(210-x)
divide by 10
32(210+x) = 52(210-x)
6720 +32x = 10920-52x
84x = 4200
x = 50
wind speed = 50 mph