Flying against the wind, an airplane travels 3800 kilometers in 4 hours. Flying with the wind, the same plane travels 3750 kilometers in 3 hours. What is the rate of the plane in still air and what is the rate of the wind?

---- velocity of wind

--- velocity of airplane

Step-by-step explanation:

Given

velocity of airplane

velocity of wind

Flying with the wind, the distance (d) is:

Where d and t are distance travel and time spent with the wind

So:

Divide by 3

Flying against the wind, the distance (d) is:

Where d and t are distance travel and time against with the wind

So:

Divide by 4

Make the subject

Substitute: in

Collect like terms

Divide by 2

Substitute in

intensity of the vector is v= √37 ≈ 6.08 units and make angle ∡α ≈ 9.46° with east direction

step-by-step explanation:

required vector is consists of the two componentsvx= 2+4=6 units   and vy= 1 unit and vx ⊥ vywe will use pythagorian theorem to find intensity of the vector vv∧2 = vx∧2 + vy∧2 => v = √vx∧2 + vy∧2 = √6∧2 + 1∧2 = √36+1 = √37 ≈ 6.08 unitsthe angle ∡α between vector and east direction we wil find with tanαtanα = 1/6 => α = arc tanα = arc 1/6 => α ≈ 9.46°

hope this