Question

When a plane flies into the wind, it can travel 3000mi in 6 hr. When it flies with the wind, it can travel the same distance in 5 hr. Find the rate of the plane in still air and the rate of the wind.

Answer 1

x = Rate without wind
y = Rate of the wind

T = D/R

6 = 3000/(x - y)
6(x - y) = 3000
6x - 6y = 3000

5 = 3000/(x + y)
5(x + y) = 3000
5x + 5y = 3000

Solve simultaneously,
6x - 6y = 3000
5x + 5y = 3000

5 *(6x - 6y = 3000)= 30x - 30y = 15,000
6 *(5x + 5y = 3000)= 30x + 30y = 18,000

30x - 30y = 15,000
30x + 30y = 18,000
60x = 33,000
x = 550 rate of the plane in still air

5x + 5y = 3000
x = 550
5(550) + 5y = 3000
2750 + 5y = 3000
5y = 250
y = 50 rate of the wind