Question

a jet travels at 610 mi/hr relative to the air. it takes the jet 1.6h longer to travle the 3660 mi from London to Washington DC against the wind than it takes from Washington to London with the wind. find the velocity of the wind?

Answer 1

Lets say velocity of wind is V and with the wind jet takes T hrs. then against the wind it will take (T + 1.6) hrs.
Also with the wind equivalent velocity will be (610 + V) miles/hr and against the wind equivalent velocity will be (610 - V)

So,
(610 + V) * (T) = 3660 .....(1)
(610 - V) * (T + 1.6) = 3660 .....(2)

From (1) and (2)
(610 + V) * (T) = (610 - V) * (T + 1.6)
610T + VT = 610T - VT + 976 - 1.6V
VT = -VT + 976 - 1.6V
2VT = 976 - 1.6V
VT = 488 - 0.8V ......(3)

Rewrite (1)
610T + VT = 3660

Substitute VT from (3)
610T + 488 - 0.8V = 3660
610T - 0.8V = 3172
305T - 0.4V = 1586
305T = 1586 + 0.4V .....(4)

Multiply by 305 in (1)
(610 + V) (305T) = 305 * 3660

Substitute 305T from (4)
(610 + V)(1586 + 0.4V) = 305 * 3660

Clearly we got quadratic equation of V.
Simply the equation and we get-
0.4$V^{2}$ + 1830V - 150670 = 0

Using shridharacharya method
V ≈ 83.87 miles/hr