A light air craft flies form A to B, 450km away, and back from B to A in a total time of 5 1/2 hours. suppose that during the whole journey there is a constant wind blowing from A to B. if the speed of the aircraft in still air is 165km per hour, find the speed of the wind.
Answers
let the speed of wind from a to b is " v " km/hr
the speed of aircraft is 165 km/hr
distance b/w a & b is 450 km .
let time taken from a to b is " t " hrs
then tine taken from b to a = ( 5.5 - t ) hrs.
so ,
the wind is blowing from a to b , so it will push the aircraft while it is going from a to b .
the wind will oppose the aircraft when it goes from b to a .
a to b
speed = dist / time
165 + v = 450 / t ------ (1)
b to a
speed = dist / time
165 - v = 450 / ( 5.5 - t ) -------- (2)
add equation 1 & equation 2
165 + v + 165 - v = 450/t + 450/(5.5 - t)
330 = 450/t + 450/(5.5-t)
solving it you'll get a quadratic equation
330t^2 - 1815t + 2475 = 0
solving it you will get
t = 3 & 2.5
take 3 .
put t = 3 in either equation 1 or 2 & calculate value of wind speed .
165 + v = 450 / 3
v = 150 - 165 = - 15 kmph which is not possible .
as speed can't be negative
so take t = 2.5
v + 165 = 450 / 2.5
v = 180 - 165 = 15kmph
which is possible and in this case correct .
wind speed is 15 km/hr .