### Math Notes

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#### Algebra Solutions

##### Topics || Problems

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 $$v_{wind} = \frac{2000}{4} - 535.71 = 35.71 mph$$