Question 571025
I will rewrite this so it makes sense:
;
Johnny went head wind (east to west I believe) from Miami to San Francisco 2100 miles in 5.6 hours.
 When this other person (a girl) went tail wind (west to east) from San Francisco to Miami 2100 miles too but only took 4.8 hours...
:
what is the air speed and the wind speed? 
:
Let s = speed in still air
let w = rate of the wind
then
(s-w) = effective speed against the wind
and
(s+w) = effective speed with the wind
;
Write a distance equation for each trip; dist = time * speed
:
5.6(s-w) = 2100
4.8(s+w) = 2100
Simplify this, divide the 1st equation by 5.6 and the 2nd equation by 4.5, resulting in:
s - w = 375
s + w = 437.5
--------------- adding eliminates w, find s
2s = 812.5
s = 812.5/2
s = 406.25 mph is the speed in still air
then
406.25 + w = 437.5
w = 437.5 - 406.25
w = 31.25 mph is the speed of the wind
;
:
You can confirm this by replacing s and w in the original equations and doing the math