Question

raju during his journey travels for 20 mins at a speed of 30km/hr, another 30mins at a speed of 50km/hr . what is his average speed? ​

Answer 1

Answer:

Step-by-step explanation:

Given,

Speed at 1st journey = 30 km/h

Time taken in 1st journey = 20 mins = 20/60 = 1/3

Speed at 2nd journey = 50 km/h

Time taken in 1st journey = 30 mins = 30/60 = 1/2

To Find,

Average Speed

Formula to be used,

Distance traveled = Speed × Time

Average speed = Total distance/Total time

Solution,

Distance traveled in 1st journey = Speed × Time

⇒ Distance traveled in 1st journey = 30 × 1/3

⇒ Distance traveled in 1st journey = 10 km

Now,

Distance traveled in 2nd journey = Speed × Time

⇒ Distance traveled in 2nd journey = 50 × 1/2

⇒ Distance traveled in 2nd journey = 25 km

Then,

⇒ Total distance = 10 + 25 = 35 km

⇒ Total time = 1/3 + 1/2 = 5/6

Now, We know that

Average speed = Total distance/Total time

⇒ Average speed = 35/(5/6)

⇒ Average speed = 35 × 6/5

⇒ Average speed = 42 km/h

Hence, the average speed is 42 km/h.

Answer 2

Step-by-step explanation:

$\frak Given = \begin{cases} &\sf{The\ speed\ at\ 1st\ journey\ =\ 30km/h.} \\ &\sf{The\ time\ taken\ in\ 1st\ journey\ =\ 20mins\ =\ \dfrac{20}{60}\ =\ \dfrac{1}{3}.} \\ &\sf{The\ speed\ at\ 2nd\ journey\ =\ 50km/h.} \\ &\sf{The\ time\ taken\ in\ 2nd\ journey\ =\ 30mins\ =\ \dfrac{30}{60}\ =\ \dfrac{1}{2}.} \end{cases}$

To find:- We have to find the average speed ?

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$\frak{\underline{\underline{\dag As\ we\ know\ that:-}}}$

$\sf{Distance\ travelled\ =\ Speed\ \times\ Time.}$

$\sf{Average\ speed\ =\ \dfrac{Total\ distance}{Total\ time}}$

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$\frak{\underline{\underline{\dag By\ substituting\ the\ values,\ we\ get:-}}}$

$\sf \therefore {\underline{Distance\ travelled\ in\ 1st\ journey:-}}$

$\sf : \implies {Speed\ \times\ time} \\ \\ \sf : \implies {30\ \times\ \dfrac{1}{3}} \\ \\ \sf : \implies {\purple{\underline{\boxed{\bf 10km.}}}}\bigstar$

$\sf \therefore {\underline{Distance\ travelled\ in\ 2nd\ journey:-}}$

$\sf : \implies {Speed\ \times\ time} \\ \\ \sf : \implies {50\ \times\ \dfrac{1}{2}} \\ \\ \sf : \implies {\purple{\underline{\boxed{\bf 25km.}}}}\bigstar$

So here:-

• Total distance = 10 + 25 = 35km.
• Total time = 1/3 + 1/2 = 5/6.

$\sf \therefore {\underline{Now,\ finding\ average\ speed:-}}$

$\sf : \implies {Average\ speed\ =\ \dfrac{Total\ distance}{Total\ time}} \\ \\ \sf : \implies {\dfrac{35}{(5/6)}} \\ \\ \sf : \implies {35\ \times\ \dfrac{6}{5}} \\ \\ \sf : \implies {\purple{\underline{\boxed{\bf 42km/h.}}}}\bigstar$

Hence:-

$\sf \therefore {\underline{The\ average\ speed\ is\ 42km/h.}}$