Question

A train travels the first 30 km of its journey with a speed of 60 km h and the next
30 km of its journey with a speed of 40 km h'. Calculate:
(i) the total time of the journey
(ii) the average speed of the train.​

Answer 1

Given :

• A train travels the first 30 km of its journey with a speed of 60 km/h and the next
• 30 km of its journey with a speed of 40 km/hr.

To Find :

• The total time of the journey
• The average speed of the train

Solution :

⚽ Case (i) :

• Distance travelled by the train = 30 km
• Speed of the train = 60 km/hr

⎈ Finding the time taken by the train for first 30 km:

→ Time taken = Distance travelled ÷ Speed of train

→ Time taken = 30 ÷ 60

→ Time taken = 3 ÷ 6

→ Time taken = 1 ÷ 2 hr

• Hence, the time taken by the train for first 30 km is 1/2 hours.

⚽ Case (ii) :

• Distance travelled by the train = 30 km
• Speed of the train = 40 km/hr

⎈ Finding the time taken by the train for next 30 km :

᠉ Time taken = Distance travelled ÷ Speed of train

᠉ Time taken = 30 ÷ 40

᠉ Time taken = 3 ÷ 4 hr

• Hence, the time taken by the train for next 30 km is 3/4 hours.

⌬ Finding the total distance travelled by the train :

➻ Total distance travelled by the train = distance travelled for first 30 km + distance travelled for next 30 km

➻ Total distance travelled by the train = 30 + 30

➻ Total distance travelled by the train = 60 km

• Hence, the total distance travelled by the train is 60 km.

⌬ Finding the total time taken by the train :

➺ Total time taken = time taken for first 30 km + time taken for next 30 km

➺ Total time taken = 1/2 + 3/4

➺ Total time taken = 0.5 + 0.75

➺ Total time taken = 1.25 hours

• Hence, the total time taken by the train is 1.25 hours.

❍ Now, let's calculate the average speed of the train :

⋙ Average Speed = Total distance ÷ Total time

⋙ Average Speed = 60 ÷ 1.25

⋙ Average Speed = 48 km/hr

• Hence,the average speed of the train is 48 km/hr.

Answer 2

$\large \color{purple} \bf Solution$

$\\ \sf \dfrac{60km \: hr}{30 \: km} = (1)$

$\\ \sf \dfrac{40km \: hr}{30 \: km \ } = (ll)$

Let's find Total time..

For Uniform speed :

$\\ \implies \sf \: s = \dfrac{d}{t}$

$\\ \implies \sf \: t = \dfrac{d}{s}$

$\\ \implies \sf \: t = \dfrac{30}{60}$

$\\ \implies \sf \: t = \dfrac{1}{2} \: hr \: ....(1)$

$\\ \implies \sf \: s_{2} = \dfrac{d_{2} }{ t_{2} } ....(ll)$

$\\ \implies \sf t_{2} = \dfrac{ d_{2} }{ s_{2}}$

$\\ \implies \dfrac{ \cancel3 \cancel0}{ \cancel4 \cancel0}$

$\\ \sf \implies t _{2} = \dfrac{3}{4} hr$

$\\ \sf \: total \: time = t_{1} + t_{2} = ( \dfrac{1}{2} + \dfrac{3}{4} )hr$

$\\ \implies \sf \dfrac{84 + 6}{8} = \dfrac{10}{8}$

30 minutes + 45 minutes

= 75 minutes.

Now let's find Speed

Formula used

$\implies \sf \: speed = \dfrac{total \: distance}{total \: time}$

$\\ \implies \sf \dfrac{60 \: km}{ \dfrac{10}{8 \: } hr}$

$\\ \implies \sf \dfrac{6 \cancel0 \times 8 \: km}{1 \cancel0 \: hr}$

$\bf \implies \color{blue}48km / hr$

Hence We got

• Time = 75 minutes

• Speed = 48 km / hr