Question

an airplane can travel 380 miles per hour in the air if it travels 2562 miles with the wind in the same length of time it travels 1998 miles against the wind, what is the speed of the wind?

Answer 1

Given

380 miles per hour

2562 miles with the wind

1998 miles against

Procedure

v = speed

v = 380 miles per hour

w = wind

v1 = v + w

v2 = v - w

t = same length of time

`\begin{gathered} x_1=v_1t \\ x_2=v_2t \\ \\ (x_1)/(v_1)=(x_2)/(v_2) \\ \\ x_1(v_2)=x_2v_1 \\ x_1v_2-x_2v_1=0 \\ 2562(380-w)-1998(380+w)=0 \\ 973560-2562w-759240-1998w=0 \\ 214320-4560w=0 \\ w=(214320)/(4560) \\ w=47 \end{gathered}`

The answer would be w = 47 miles per hour