Problema Solution
An airplane pilot finds he can go 72 miles in 35 minutes when traveling with the wind. He finds it takes him 44 minutes at the same airspeed to go 57 miles against the same wind. Find the speed of the wind and the airspeed of the plane.
Answer provided by our tutors
speed is easiest to calculate in mph since we are given minutes must convert to hours so divide by 60 as there are 60 minutes in an hour.
so we need 2 variables actual speed a and head wind speed hw.
(a + hw) * 35/60 = 72
(a - hw) * 44/60 = 57
we add hw in the first equation because our speed will increas due to the headwind pushing the plane and in the second problem we must subtract as it will decrease the speed.
next we must solve for one variable in terms of the other.
using eqn 2
a =57*60/44 + hw
now substituting this value in for a into equation 1 we get
(57*60/44 + hw + hw)*35/60 = 72
simplifying we get
70/60 *hw + 57*35/44 = 72
hw = (72-57*35/44)*60/70
hw = 22.8506 mph
now pluging this into eqn 2 we can solve for a
(a - 22.8506)*44/60 = 57
a*44/60 =57+(22.8506*44/60)
a = (57 + (22.8506*44/60))*60/44
a = 100.5779 mph
so the airspeed is 100.58 mph
and the wind speed is 22.85 mph