A jet fighter travels 2000 miles in 3.5 hours with the tail wind. The return trip, into the wind takes 4 hours. Find the wind speed and the jet speed.
Solution:
Let x be the velocity of the wind
\( v= \frac{d}{t}\)
\( v_{total} = v_{jet} + v_{wind}\) : With the wind
\( v_{total} = v_{jet} - v_{ wind }\) : Against the wind
\( \frac{2000}{3.5} = v_{jet} + v_{ wind }\) : With the wind (1)
\( \frac{2000}{4} = v_{jet} - v_{ wind }\) : Against the wind (2)
Add the two equations (1 and 2)
\(\frac{7500}{7} = 2v_{jet}\)
Thus, the velocity of the jet is 535.71 mph
And the velocity of the wind is \(v_{wind} = \frac{2000}{4} - 535.71 = 35.71 mph\)