find the velocity

Question

A plane can fly 370 mph in still air. If it can fly 215 miles downwind in the same amount of time it can fly 155 miles upwind, find the velocity of the wind.



Answer 1

370 mph in still wind, with no wind

215 miles down wind, with the wind

155 miles up wind, against the wind

what is the wind speed?

d=rt

distance = rate of speed times time

215 = (370+w)t

155 = (370-w)t

2 equations 2 unknowns

solve by substitution elimination or matrix algebra

divide one equation by the other to eliminate one variable t

215/155 = (370+w)/(370-w)= 43/31

cross multiply

(370+w)31 = (370-w)43

370(31) + 31w = 370(43) -43w

74w = 370(43)-370(31) = 370(12)

w = 370(12)/74 = 60 mph = wind speed

215 = (360+60)t = 420t

t = 215/420 = 43/85 = about .51hours

155 = (360-60)t = 300t

t = 155/300 = 31/60 = about .51

time = about 1/2 hour

still a slight arithmetic error or 2 somewhere.

very close though

time is exactly 1/2 hour=.5 , not .51

215 = (370+60)(1/2) = 430/2 = 215

155 = (370-60)(1/2) = 310/2 = 155