Question

on a 60km track strain travels the first 30km with a uniform speed of 30 km-¹ how fast must the train travel the next 30km so as to average 40kmh-¹ for the entire trip?​

Answer 1

Answer:

60 km/h

Explanation:

As per the provided information in the given question, we have :

• On a 60 km track a train travels the first 30 km with a uniform speed of 30 km/h.

We've to calculate the speed of the train needed by the train to travel the next 30km so as to average 40 km/h.

Let us suppose the required speed as x km/h.

Now, according to the question, on a 60 km track a train travels the first 30 km with a uniform speed of 30 km/h. So, here :

• Distance covered in first time = 30 km
• Speed = 30 km/h

And, in the second time :

• Distance covered in second time = (60 – 30) km = 30 km
• Speed = x km/h

Now, we know that average speed is the total distance travelled by total time taken. Here total distance travelled is 60 km. We've to find total time taken. Total time taken will be the sum of time taken to cover the first 30 km and then time taken to cover the second 30 km. We know that,

⠀⠀⠀⠀⠀⠀○ Time = Distance ÷ Speed

So,

$\dashrightarrow \rm{\quad { Time_{(Total)} = \Bigg ( \cancel{\dfrac{30}{30}} + \dfrac{30}{x} \Bigg ) \; h }}$

$\dashrightarrow \rm{\quad { Time_{(Total)} = \Bigg ( 1 + \dfrac{30}{x} \Bigg ) \; h }}$

$\dashrightarrow \bf\quad { Time_{(Total)} = \Bigg ( \dfrac{x + 30}{x} \Bigg ) \; h }$

Now, we as we know that,

$\bigstar \quad\underline{\boxed {\bf Speed_{(Avg)} = \dfrac{Distance_{(Total)}}{Time_{(Total)}} }}$

• Average speed = 40 km/h

$\dashrightarrow \rm{\quad { 40 = 60 \div \Bigg ( \dfrac{x + 30}{x} \Bigg ) }}$

$\dashrightarrow \rm{\quad { 40 = 60 \times \Bigg ( \dfrac{x}{x + 30} \Bigg ) }}$

$\dashrightarrow \rm{\quad {\cancel{\dfrac{ 40}{60}} = \Bigg ( \dfrac{x}{x + 30} \Bigg ) }}$

$\dashrightarrow \rm{\quad {\dfrac{2}{3} = \Bigg ( \dfrac{x}{x + 30} \Bigg ) }}$

Now, by cross multiplication,

$\dashrightarrow \rm{\quad {2(x + 30) = 3x }}$

$\dashrightarrow \rm{\quad {2x + 60= 3x }}$

$\dashrightarrow \rm{\quad {60 = 3x - 2x }}$

$\dashrightarrow \quad \underline{\boxed{\bf 60 \; km \: h^{-1}= x }}$

Therefore, the train must run with 60 km/h for the next 30 km so as to average 40 km/h for the entire trip.

Answer 2

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