SOLUTION: A pilot found that it took 3/4 as long to travel 100 kilometers with a 30 km/hr tailwind as it took to travel the same distance with a 30 km/hr headwind. Find the speed of the pla

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Question 821894: A pilot found that it took 3/4 as long to travel 100 kilometers with a 30 km/hr tailwind as it took to travel the same distance with a 30 km/hr headwind. Find the speed of the plane in still air.
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
A pilot found that it took 3/4 as long to travel 100 kilometers with a 30 km/hr tailwind as it took to travel the same distance with a 30 km/hr headwind.
Find the speed of the plane in still air.
:
Let s = speed of plane in still air
then
(s+30) = effective ground speed with the wind
and
(s-30) = effective ground speed against the wind
:
let d = the one way distance (we don't need to know the distance)
:
Write a time equation, time = dist/speed
use the decimal equiv of 3/4
:
with wind time = 3/4 against wind time
= .75()
=
Cross multiply
d(s-30) = .75d(s+30)
divide both sides by d
s-30 = .75(s+30)
s - 30 = .75s + 22.5
s - .75s = 22.5 + 30
.25s = 52.5
s = 52.5/.25
s = 210 km/h plane speed in still air
:
:
You can check this using a distance of 100 km
= *