SOLUTION: Mr. Carlson took 2.5 hours to fly his airplane a distance of 360 miles against a steady wind. It took him 2 hours to make the return trip with the wind. Find Mr. Carlons rate in c
Question 188293: Mr. Carlson took 2.5 hours to fly his airplane a distance of 360 miles against a steady wind. It took him 2 hours to make the return trip with the wind. Find Mr. Carlons rate in calm air, and the rate of the wind . use r=d/t.
answer: Mr. Carlson files 162 miles per hourin calm air; the wind is blowing at a rate of 18 mph.
need a full break down of how my book got this answer
You can put this solution on YOUR website! Mr. Carlson took 2.5 hours to fly his airplane a distance of 360 miles against a steady wind.
It took him 2 hours to make the return trip with the wind.
Find Mr. Carlson's rate in calm air, and the rate of the wind. use r=d/t.
:
Let r = his speed in calm air
Let w = the speed of the wind
then
(r+w) = his ground speed with the wind
and
(r-w) = his ground speed against the wind
:
Write a distance equation for each trip: Dist = time * speed
2.5(r-w) = 360
2.0(r+w) = 360
Simplify both equations, divide the 1st by 2.5 and the second by 2, results:
r - w = 144
r + w = 180
-------------Addition eliminates w, find r
2r = 324
r =
r = 162 mph in still air
:
and using r + w = 180, find w
162 + w = 180
w = 180 - 162
w = 18 mph is the wind
;
:
Check solutions in the 1st original equation
2.5(162 - 18) =
2.5(144) = 360 mi, confirms our solutions
