Question

A plane flies from Los Angeles west to Paradise Isle and returns. During both flights there is a steady upper air wind from the west at 80 mph. If the trip west to Paradise Isle took 17 hours and the return trip to Los Angeles took 13 hours, what was the plane's average airspeed?

Answer 1

Answer: $589.33\ mph$

Step-by-step explanation:

Given

Trip form Los Angeles west to Paradise Isle took 17 hours and return trip took 13 hours.

Wind from west is 80 mph

Distance traveled is same in both the cases. During the first Journey, wind causes an upstream and for second half, it creates a downstream.

Suppose the speed of plane is

$\Rightarrow (v-80)17=(v+80)13\\\Rightarrow 17v-1360=13v+1040\\\Rightarrow 4v=2400\\\Rightarrow v=600\ mph$

Suppose the distance is x

$\Rightarrow x=(600-80)\times 17\\\Rightarrow x=520\times 17\\\Rightarrow x=8840\ \text{miles}$

Average speed is

$\Rightarrow v_{avg}=\dfrac{x+x}{17+13}\\\\\Rightarrow v_{avg}=\dfrac{2\times 8840}{30}\\\\\Rightarrow v_{avg}=589.33\ mph$

Answer 2

Answer:

The speed of plane is 600 mph.

Step-by-step explanation:

Let the distance is d.

Speed of wind , u = 80 mph

Time, t = 17 hours

time, t'= 13 hours

Let the speed of airplane is v.

distance = speed x time

d = (v + u) x 13= (v - u) x 17

(v + 80) x 13 = (v - 80) x 17

13 v + 1040 = 17 v - 1360

4 v = 2400

v = 600 mph