A bus covers the first half of the total distance 6 km at a speed ' u ' and the second half at speed of 30 ~km ~h ⁻¹ . If the average speed is 15 ~km ~h ⁻¹ the value of ' u ' is:

Step-by-step solution

Let the total distance be D = 6 km. The bus covers the first half distance d = 3 km at speed u and the second half distance d = 3 km at speed v = 30 km h ⁻¹ . The time taken for the first half is t₁ = d u = 3 u . The time taken for the second half is t₂ = d v = 3 30 = 1 10 h. The average speed v_ avg is defined as the total distance divided by the total time: v_ avg = D t₁ + t₂ = 6 3 u + 1 10 Given v_ avg = 15 km h ⁻¹ , we have: 15 = 6 3 u + 1 10 Dividing both sides by 3: 5 = 2 3 u + 1 10 Rearranging the terms: 3 u