Problema Solution
Against the wind a small plane flew 280 miles in 1 hour and 10 min. the return trip took only 50 min. What was the speed of the wind? What was the speed of the plane in the air?
Answer provided by our tutors
let
d = 280 miles
t1 = 1 hour 10 min = 1 + 10/60 = 7/6 hours the time of the rip against wind
t2 = 50 min = 50/60 = 5/6 hours the time of the return trip (with the wind)
w = the speed of the wind
v = the speed of the plane in still air
v - w = the speed of the plane flying against the wind
v + w = the speed of the plane flying with the wind
since speed = distance/time we have
v - w = d/t1
v + w = d/t2
thus we have the system of equations
v - w = 280/(7/6)
v + w = 280/(5/6)
by solving we find
v = 288 mph the speed of the plane in still air
w = 48 mph the peed of the wind
click here to see the step by step solution of the system of equations