Wind drift

The plane flies at 780 km/h, passing distance 1200 kilometers with the wind and once again against the wind for 3 h 5 min. What is the wind speed?

Final Answer:

w = 35.5649 km/h

v = 780 km/h a = 1200 km T = 3 : 5 = 3 h r 5 m i n = 3 + \frac{5}{6 0} = 3.0833 h r ≐ 3.0833 t_{1} + t_{2} = T (v + w) t_{1} = a (v - w) t_{2} = a (v + w) t_{1} = a (v - w) (T - t_{1}) = a (v - w) (T - \frac{a}{v + w}) = a (v - w) \cdot (T \cdot (v + w) - a) = a \cdot (v + w) (780 - w) \cdot (3.0833333333333 \cdot (780 + w) - 1200) = 1200 \cdot (780 + w) - 3.0833333331393 w^{2} + 3900 = 0 3.0833333331393 w^{2} - 3900 = 0 w_{1, 2} = \pm 3899.99999998 / 3.0833333331393 = \pm 35.564938703 w_{1} = 35.564938703 w_{2} = - 35.564938703 w = w_{1} = 35.5649 ≐ 35.5649 km/h t_{1} = \frac{a}{v + w} = \frac{1 2 0 0}{7 8 0 + 3 5 . 5 6 4 9} ≐ 1.4714 h t_{2} = \frac{a}{v - w} = \frac{1 2 0 0}{7 8 0 - 3 5 . 5 6 4 9} ≐ 1.612 h Verifying Solution: a_{1} = (v + w) \cdot t_{1} = (780 + 35.5649) \cdot 1.4714 = 1200 km a_{2} = (v - w) \cdot t_{2} = (780 - 35.5649) \cdot 1.612 = 1200 km T_{2} = t_{1} + t_{2} = 1.4714 + 1.612 = \frac{3 7}{1 2} ≐ 3.0833 h

Did you find an error or inaccuracy? Feel free to send us. Thank you!

Tips for related online calculators

Are you looking for help with calculating roots of a quadratic equation?
Do you have a linear equation or system of equations and are looking for its solution? Or do you have a quadratic equation?
Do you want to convert velocity (speed) units?
Do you want to convert time units like minutes to seconds?

algebra

Units of physical quantities

themes, topics

Grade of the word problem