Question

On a track of lenght 100km, the train covers first 30km with a constant speed of 30kmh-1 .What should be the speed of the train for the next 70km so that the average speed of the train remains 50kmh-1 for the entire trip?​

Answer 1

Answer:

• 70 km/h

Step-by-step explanation:

Given:

• Total distance travelled = 100 km
• Distance, d₁ = 30 km
• Speed at first 30 km, v₁ = 30 km/h
• Distance, d₂ = 70 km
• Average speed = 50 km/h

To Find:

• The speed of the train for the next 70 km.

Solution:

Let the speed of the train for the next 70 km be v₂

Now,

• Time taken to travel first 30 km, t₁ = Distance/Speed
• Time taken to travel first 30 km, t₁ = d₁/v₁
• Time taken to travel first 30 km, t₁ = 30/30
• Time taken to travel first 30 km, t₁ = 1 h

• Time taken to travel next 70 km, t₂ = Distance/Speed
• Time taken to travel next 70 km, t₂ = d₂/v₂
• Time taken to travel next 70 km, t₂ = 70/v₂

After that,

• Average speed = Total distance travelled/Total time taken
• 50 = 100/( t₁ + t₂ )
• 50 = 100/( 1 + 70/v₂ )
• 50 = 100/( (v₂ + 70)/v₂ )
• 50 = 100v₂/(v₂ + 70 )
• 50(v₂ + 70 ) = 100v₂
• 50v₂ + 3500 = 100v₂
• 3500 = 100v₂ - 50v₂
• 3500 = 50v₂
• v₂ = 3500/50
• v₂ = 350/5
• v₂ = 70 km/h

∴ The speed of the train for the next 70 km = 70 km/h

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