Word Problem on Distance and Direction Covered by a Vehicle

Topic : Distance Travelled by a Vehicle along a Direction.

Question : A jet airplane, traveling at an average speed of 420 miles per hour in still air, flew 240 miles and back in 1 hour and 10 minutes. What was the average speed of the wind in miles per hour?

Solution :
Let the average speed of air = x miles/hour
With the direction of the wind, the speed of the aircraft = 420 + x miles/hour
Against the direction if the wind the speed of the aircraft = 420- x miles/hour
Time taken to fly with the wind = 240/ 420+x hour
Time taken to fly against the wind = 240/420 – x hour.
Given,
240/420+x + 240/ 420 –x =1 1/6 = 7/6 hour
240( 1/420+x + 1/ 420-x ) =7/6
240( 420-x + 420 + x)/ 420 ^2 –x^2 = 7/6
240x 2 x 420 x6 / 7 =420^2 – x^2
240x 720 = 176400- x^2
x^2 = 176400- 172800
= 3600
x = 60 miles/hour.
Average speed of air = 60 miles/hour.