The distance between cities A and B is 1600 km. The plane from A to B flew at a speed 80 km / h

The distance between cities A and B is 1600 km. The plane from A to B flew at a speed 80 km / h higher than back from B to A. From A to B the plane flew 1 hour faster than from B to A. At what speed did the plane fly from A to B and with what speed from B to A?

Let the plane flew from city B to city A at a speed of x km / h, then from city A to city B it flew at a speed of (x + 80) km / h. The distance of 1600 kilometers from A to B the plane flew in 1600 / (x + 80) hours, and from B to A in 1690 / x hours. By the condition of the problem, it is known that the plane spent less time on the way from A to B than on the way from B to A by (1600 / x – 1600 / (x + 80)) hours or 1 hour. Let’s make an equation and solve it.

1600 / x – 1600 / (x + 80) = 1;

O.D.Z. x ≠ 0; x ≠ -80.

1690 (x + 80) – 1600x = x (x + 80);

1600x + 128000 – 1600 = x² + 80x;

x² + 80x – 128000 = 0;

D = b² – 4ac;

D = 80² – 4 * 1 * (-128000) = 518400; √D = 720;

x = (-b ± √D) / (2a);

x1 = (-80 + 720) / 2 = 640/2 = 320 (km / h) – speed from B to A;

x2 = (-80 – 720) / 2 = -400 – the speed cannot be negative.

x + 80 = 320 + 80 = 400 (km / h) – speed from A to B.

Answer. From A to B the plane flew at a speed of 400 km / h, and from B to A – 320 km / h.