Problema Solution
It took an airplane 2 hours to fly 600 miles against a headwind. The return trip with the wind took 1 2/3 hours. Find the speed of the plane with no wind and the windspeed.
Answer provided by our tutors
let
v = the speed of the plane with no wind
w = the windspeed
d = 600 mi the trip in each direction
t1 = 2 hr the time of the travel against the headwind
t2 = 1 2/3 = 5/3 hr the time of the travel with the wind
the speed of the plane when traveling with the wind is: v + w
the speed of the plane when traveling against a headwind is: v - w
since distance = speed*time we have
traveling with the wind:
t2(v + w) = d
(5/3)(v + w) = 600 multiply both sides by 3/5
v + w = 360
raveling against a headwind:
t1(v - w) = d
2(v - w) = 600 divide both sides by 2
v - w = 300
by solving the system of equations
v + w = 360
v - w = 300
we find
v = 330 mph
w = 30 mph
click here to see the step by step solution of the system of equations
the speed of the plane with no wind is 330 mph.
the windspeed is 30 mph.