Problema Solution
Tammy is flying an antique airplane to the air show. If her plane can travel 150 miles in one hour with the wind and 90 miles in twice the time heading into the wind, how fast is the plane moving without the wind?
Answer provided by our tutors
let
d1 = 150 mi the distance traveled with the wind
t1 = 1 hr the time traveling with the wind
d2 = 90 mi the time traveling into the wind
t2 = 2*t2 = 2*1 = 2 hr the time traveling into the wind
w = the speed of the wind, w>0
v = the speed of the plane without the wind, v>0
since speed = distance/time we have:
traveling with the wind the speed of the plane is: v + w
v + w = d1/t1
v + w = 150/1
v + w = 150 mph
traveling against the wind the speed of the plane is: v - w
v - w = d2/t2
v - w = 90/2
v - w = 45 mph
by solving the system of equations:
v + w = 150
v - w = 45
we find:
v = 97.5 mph
w = 52.5 mph
click here to see the step by step solution of the system of equations:
the speed of the plane without the wind is 97.5 mph.