A bus travels at 30 km/h for the first 2 h of a journey and then travels at 50 km/h for the…

Step-by-step solution

1. 1. Given Data

   First part: speed S₁ = 30 km/h, time T₁ = 2 h.

   $$S_1 = 30 \text{ km/h}, T_1 = 2 \text{ h}$$

2. 2. Given Data

   Second part: speed S₂ = 50 km/h, time T₂ = 2 h.

   $$S_2 = 50 \text{ km/h}, T_2 = 2 \text{ h}$$

3. 3. Distance Formula

   Distance is calculated as speed multiplied by time.

   $$D = S \times T$$

4. 4. Calculate Distances

   Distance for first part D₁ = S₁ × T₁ = 30 km/h × 2 h = 60 km.

   $$D_1 = 30 \times 2 = 60 \text{ km}$$

5. 5. Calculate Distances

   Distance for second part D₂ = S₂ × T₂ = 50 km/h × 2 h = 100 km.

   $$D_2 = 50 \times 2 = 100 \text{ km}$$

6. 6. Ratio of Speeds

   Ratio of speeds S₁ : S₂ = 30 : 50 = 3 : 5.

   $$S_1 : S_2 = 30 : 50 = 3 : 5$$

7. 7. Ratio of Distances

   Ratio of distances D₁ : D₂ = 60 : 100 = 3 : 5.

   $$D_1 : D_2 = 60 : 100 = 3 : 5$$

8. 8. Final Answer

   The ratio of speeds is 3:5 and the ratio of distances is 3:5.

   $$S_1:S_2 = 3:5, D_1:D_2 = 3:5$$

9. 9. Yaad rakho / Key takeaway

   When time is constant, distance is directly proportional to speed.

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