An airplane travels 4362 km against the wind in 6 hours and 5322 km with the wind in the same amount of time. What is the rate of the plane in still air ?
Choose the correct choice from the following:
A) 803km/hr
B) 805km/hr
C) 809km/hr
D) 807km/hr
E) 806km/hr
Let the speed of the air plane in still air be x km/hr   And the speed of the wind be y km/hr.   Then speed of the airplane going with the wind = (x + y) km/hr   and speed of the airplane going against the wind = (x - y) km/hr.   We know that,   Distance = Speed × Time   or, Speed = Distance   Time   According to the problem,   An airplane travels 4362 km against the wind in 6 hours   x - y = 4362/6   or, x - y = 727 ----------- (1)   Again, the airplane travels 5322 km with the wind in the same amount of time i.e. 6 hours   x + y = 5322/6   or, x + y = 887 ----------- (2)   Now add (1) and (2) we get,   x - y = 727   x + y = 887   2x = 1614   or, 2x/2 = 1614/2, (807km/hrivide both sides by 2)   or, x = 807   Now substitute the value of value of x = 807 in equation (2) we get,   807 + y = 887   -807 -807, (Subtract 407 from both sides)   y = 80   Answer: Rate of the plane in still air = 807 km/hr   correct answer 807km/hr)807 km/hr
<result>D</result>
An airplane travels 4362 km against the wind in 6 hours and 5322 km with the wind in the same amount of time. What is the rate of the plane in still air ?