Question

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?

Answer 1

Answer:

$V_w =1100$ ---- velocity of wind

$V_a = 150$ --- velocity of airplane

Step-by-step explanation:

Given

$V_a \to$ velocity of airplane

$V_w \to$ velocity of wind

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

$d = (V_w + V_a) * t$

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

So:

$3750 = (V_w + V_a) * 3$

Divide by 3

$1250 = (V_w + V_a)$

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

$d = (V_w - V_a) * t$

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

So:

$3800 = (V_w - V_a) * 4$

Divide by 4

$950 = (V_w - V_a)$

Make $V_w$ the subject

$V_w= 950 + V_a$

Substitute: $V_w= 950 + V_a$ in $1250 = (V_w + V_a)$

$1250 = 950 + V_a + V_a$

$1250 = 950 + 2V_a$

Collect like terms

$2V_a = 1250 -950$

$2V_a = 300$

Divide by 2

$V_a = 150$

Substitute $V_a = 150$ in $V_w= 950 + V_a$

$V_w =950 +150$

$V_w =1100$