Problema Solution
Suppose you are flying an ultralight aircraft. You fly to a nearby town, 18 miles away. With a tail wind, the trip takes one third hour. Your return flight with a head wind takes three fifths of an hour. Find the airspeed of the ultralight, and find the average wind speed.
Answer provided by our tutors
x = speed of aircraft
y = wind speed
r1 = top row equation
r2 = bottom row equation
First trip:
18/(x + y) = 1/3
(1/3)x + (1/3)y = 18
x + y = 54
Return trip:
18/(x - y) = 0.6
0.6x - 0.6y = 18
x - y = 30
=> x + y = 54
x - y = 30 r2 = -r2 + r1
=> x + y = 54
2y = 24
y = 12
Plug into top row and solve:
x + 12 = 54
x = 42
Aircraft speed: 42 mph
Wind speed: 12 mph