Two cars left point A for point B simultaneously. The first drove at a constant speed all the way

Two cars left point A for point B simultaneously. The first drove at a constant speed all the way. The second traveled the first half of the journey at a speed 11 km / h less than the first, and the second half of the journey at 66 km / h, as a result of which he arrived at point B simultaneously with the first car. Find the speed of the first car if it is known to be greater than 42 km / h.

1. Distance between points A and B: S km;

2. The duration of the trip to point A of cars is the same: T hour;

3. The first car drove all the way at a speed: V km / h;

4. Travel time: T = S / V hour;

5. The second car drove the first half of the way at a speed: V21 = V – 11 km / h;

6. He traveled the second half of the journey at a speed of V22 = 66 km / h;

7. Travel time of the second car:

T = T1 + T2 = (S / 2) / V21 + (S / 2) / 66 =

(S / 2) * (1 / (V – 11) + 1/66) = S / V;

V * (V + 55) = 132 * V – 1452;

V ^ 2 – 77 + 1452 = 0;

V12 = 77/2 + – sqrt ((77/2) ^ 2 – 1452) = 77/2 + – 11/2;

8. By the condition of the problem: V> 42 km / h;

V = (77 + 11) / 2 = 44 km / h.

Answer: the speed of the first car is 44 km / h.