Total distance = 105 km in 5 hoursS5 = S1² + 15S3 = S5/2S4 = 2(S1 + S2)S2 = S3/2Setting up the equations:From the relationships:S2 = S3/2S3 = S5/2Therefore: S2 = (S5/2)/2 = S5/4Since S5 = S1² + 15:S3 = (S1² + 15)/2S2 = (S1² + 15)/4And S4 = 2(S1 + S2) = 2(S1 + (S1² + 15)/4) = 2S1 + (S1² + 15)/2Using the constraint that the automobile covers 105 km in 5 hours:Since the speeds change at four different points with equal intervals, each speed is maintained for 1 hour.So: S1(1) + S2(1) + S3(1) + S4(1) + S5(1) = 105Substituting: S1 + (S1² + 15)/4 + (S1² + 15)/2 + 2S1 + (S1² + 15)/2 + (S1² + 15) = 105Simplifying: S1 + 2S1 + (S1² + 15)/4 + (S1² + 15)/2 + (S1² + 15)/2 + (S1² + 15) = 1053S1 + (S1² + 15)(1/4 + 1/2 + 1/2 + 1) = 1053S1 + (S1² + 15)(2.25) = 1053S1 + 2.25S1² + 33.75 = 1052.25S1² + 3S1 - 71.25 = 0Multiplying by 4: 9S1² + 12S1 - 285 = 0Using the quadratic formula: S1 = (-12 ± √(144 + 10260))/18 = (-12 ± √10404)/18 = (-12 ± 102)/18Since speed must be positive: S1 = 90/18 = 5 km/hFinding all speeds:S1 = 5 km/hS2 = (25 + 15)/4 = 10 km/hS3 = (25 + 15)/2 = 20 km/hS4 = 2(5 + 10) = 30 km/hS5 = 25 + 15 = 40 km/hVerification: 5 + 10 + 20 + 30 + 40 = 105 km Answer: For continuous travel at S5 = 40 km/h to cover 105 km: Time = Distance/Speed = 105/40 = 2.625 hours.

explain please An automobile changes speed at four different points placed at equal intervals and covers 105 km in 5 hours S1,S2,S3.S4 and S5 are the 5 different speeds. S5 is 15 more than the square of S1, half of S5 is S3 , S4 is twice the sum of S1 and S2 and S2 makes up half of S3. How many hours of continuous travel will S5 require?

explain please An automobile changes speed at four different points placed at equal intervals and covers 105 km in 5 hours S1,S2,S3.S4 and S5 are the 5 different speeds. S5 is 15 more than the square of S1, half of S5 is S3 , S4 is twice the sum of S1 and S2 and S2 makes up half of S3. How many hours of continuous travel will S5 require?