The car was moving along a straight road. He traveled the first third of the way at a speed of 70 km / h

The car was moving along a straight road. He traveled the first third of the way at a speed of 70 km / h, the second third of the way at a speed of 90 km / h, and the last third of the way at a speed equal to the average speed along the entire route. The whole journey took 4 hours. Find the time it took for the car to cover the first third of the way.

Task data: V1 (speed in the first third of the way) = 70 km / h; V2 (speed in the second third of the way) = 90 km / h; V3 (speed on the last third of the way) = Vav (average speed); t (time spent by the specified vehicle) = 4 hours.
1) Average speed: Vav = S / (t1 + t2 + t3) = S / (S / 3V1 + S / 3V2 + S / 3Vav) = 1 / (1 / 3V1 + 1 / 3V2 + 1 / 3Vav) = 1 / (1 / (3 * 70) + 1 / (3 * 90) + 1 / 3Vav) = 1 / (1/210 + 1/270 + 1 / 3Vav).
1 / Vav = 1/210 + 1/270 + 1 / 3Vav.
2 / 3Vav = 1/210 + 1/270.
2/3 Vav = 8/945.
Vav = 945 * 2 / (3 * 8) = 78.75 m / s.
2) The last third of the way: S3 = S / 3 = Vav * t / 3 = 78.75 * 4/3 = 105 km.
3) Time spent on the last third of the way: t3 = S3 / Vav = 105 / 78.75 = 1.33 (3) h = 80 minutes.
Answer: The indicated car spent 80 minutes on the last third of the way.