Question 778647
A homing device left its home to deliver a message.
 On takeoff the device encountered a tailwind of 9 mph and made the delivery in 20 minutes.
 The return trip into the wind took 40 minutes.
 How fast could the device fly in still air?
:
Let s = speed in still air
then
(s+9) = relative speed with the wind
and
(s-9) = relative speed against
:
Change 20 min to 1/3 hr. Change 40 min to 2/3 hr
:
Write a distance equation, distance there and back are the same
{{{2/3}}}(s-9) = {{{1/3}}}(s+9)
multiply both sides by 3, resulting in:
2(s-9) = s + 9
2s - 18 = s + 9
2s -s = 9 + 18
s = 27 mph speed in still air
:
:
Confirm this by finding the actual distances
{{{2/3}}}*(27-9) = 12 mi
{{{1/3}}}*(27+9) = 12 mi