Problema Solution
An airplane went 250 miles with a headwind of 15mph and 460 miles with a tailwind of 25mph the plane flew for 4 hours how fast was the plane traveling with a no wind?
Answer provided by our tutors
let
w = 15 mph the wind speed
v = the speed of the plane in still air (no wind)
d1 = 250 mi the distance traveled with a headwind
d2 = 460 mi the distance traveled with a tailwind
t = 4 h the total time of the flight
the speed of the plane with the wind is: v + w
the speed of the plane against the wind is: v - w
since speed=distance/time => time = distance/speed
d1/(v + w) + d2/(v - w) = t
250/(v - 15) + 460/(v + 15) = 4 multiply both sides by (v - 15)(v + 15)
250(v + 15) + 460(v - 15) = 4(v - 15)(v + 15)
by solving we find two solutions
v1 = 174.24 mph
v2 = 3.24 mph
click here to see the step by step solution of the equation
v2 = 3.24 mph can not be a solution of the problem since that would mean the plane is flying backward with the head wind (3.24 < 15)
the plane is traveling 174.24 mph with no wind.