Problema Solution
against the wind a small plane flew 280 miles in 1 hour and 10 minutes. The return trip took only 50 minutes. What was the speed of the wind? What was the speed of the plane in still air?
Answer provided by our tutors
let
d = 280 mi the distance traveled in each direction
t1 = 1 hr 10 min = 1 + 10/60 = 1 + 1/6 = 7/6 hr traveling against the wind
t2 = 50 min = 50/60 hr = 5/6 hr traveling with the wind
w = the speed of the wind
v = the speed of the plane in still air
since speed = distance/time we have:
traveling against the wind the speed of the plane is: v - w
v - w = d/t1
v - w = 280/(7/6)
v - w = 240
traveling with the wind the speed of the plane is: v + w
v + w = d/t2
v + w = 280/(5/6)
v + w = 336
by solving the system of equations:
v - w = 240
v + w = 336
we wind:
v = 288 mph
w = 48 mph
click here to see the step by step solution of the system of equations:
the speed of the wind is 48 mph.
the speed of the plane in still air is 288 mph.