## 25. Subsonic and Supersonic

Two pilots, Dupont and Durand, simultaneously leave the French airport Roissy and head for Kennedy Airport in New York. One of the pilots is flying a subsonic aircraft, while the other is flying a supersonic aircraft. After some time, it turned out that if the aircraft piloted by Dupont had flown twice the distance, it would have had to fly one and a half times less of the remaining distance, and that if the aircraft piloted by Durand had flown one and a half times less distance, it would have had to cover twice the remaining distance.

Which pilot was flying the supersonic aircraft?
25. Let $x$ be the distance Dupont has flown, and $x^{\prime}$ be the distance he has left to fly; similarly, $y$ be the distance Durand has flown, and $y^{\prime}$ be the distance he has left to fly.

The total distance between the airports can be expressed in four different ways:

$$
x+x^{\prime} ; \quad 2 x+x^{\prime} / 1.5 ; \quad y+y^{\prime} ; \quad y / 1.5+2 y^{\prime}
$$

By equating the first two expressions, we get $x=x^{\prime} / 3$, and by equating the last two expressions, we find

$$
y=3 y^{\prime}
$$

Thus, Dupont has flown a quarter of the total distance, while Durand has flown three quarters; therefore, the supersonic plane was piloted by Durand.