Speed of the wind for jet speed in still air 240mph and jet covers 700 miles with tailwind and same distance against the wind in total time of 6 hours is equal to 40mph.
As given in the question,
Given data:
Jet speed in still air = 240mph
Let x be the speed of the wind.
Speed with tail wind = 240 +x
Distance covered with tail wind = 700miles
Time taken by jet with tail wind
= Distance/ speed
= 700 / (240 +x) __(1)
Speed against the wind = 240 - x
Distance covered against the wind = 700miles
Time taken by jet against the wind
= Distance/ speed
= 700 / (240 - x) __(2)
Total time taken is 6 hours
[700 / (240 +x)] + [700 / (240 - x)] = 6
⇒ 700( 240 -x + 240 + x) = 6 (240 +x)(240 - x)
⇒ 700 ( 480) = 6 ( 240² -x²)
⇒ 700 (80) = 57600 -x²
⇒ x² = 57600 - 56000
⇒ x² = 1600
⇒ x = √1600
⇒ x= 40 mph
Therefore, speed of the wind for jet speed in still air 240mph and jet covers 700 miles with tailwind and same distance against the wind in total time of 6 hours is equal to 40mph.
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