Question

A man travels from Cuttack to Bhubaneshwar at the speed of 50 km per hour and reaches in 30 minutes. Then he travels from Bhubaneshwar to Puri at the speed of 60 km per hour and reaches in 1 hour. What is his average speed​

Answer 1

Answer:-

Given:

• A man travels from Cuttak to Bhubaneswar with a speed of 50 km/hr in 30 minutes.

• Then , he travels from Bhubaneswar to Puri with a speed of 60 km/h and reaches in 1 hour.

We know that,

Distance = Speed × time

So,

★ Distance travelled by the man from Cuttak to Bhubaneswar = 50 km/h × 30 min

• 1 min = 1/60 hrs → 30 min = (30/60) hrs.

⟶ Distance travelled by the man from Cuttak to Bhubaneswar = 50 km/h × 30/60 h = 25 km.

Similarly,

★ Distance travelled by the man from Bhubaneswar to Puri = 60 km/h × 1 hr = 60 km.

We know,

Average speed = Total Distance travelled/total Time taken

• Total distance travelled = 25 + 60 = 85 km.

• Total Time taken = (30/60) + 1 = (1/2) + 1 = 3/2 hrs

So,

⟶ Average speed of the man = 85/ (3/2)

⟶ Average speed of the man = 85 * (2/3)

⟶ Average speed of the man = 56.66 km/h

Answer 2

Answer :-

$\: \: \: \underline{\boxed{\sf{\green{\mapsto \: \: \: Let's \: understand \: the \: concept \: of \: this \: question}}}}$

Here the concept of Average Speed has been used. According to the formula, Average Speed is the total distance covered in total used time. We see that in this question, the man firay travels from Cuttack to Bhubaneswar with some speed in some time. Now we can calculate the distance from this. Similarly we can calculate the distance travelled in second journey from Bhubaneswar to Puri. Finally, after we get our values, we can find the required answer.

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★ Formula Used :-

$\: \: \boxed{\rm{\blue{\longrightarrow \: \: Average \: Speed, \: (v_{av}) \: = \: \dfrac{Total \: Distance}{Total \: Time}}}}$

$\: \: \boxed{\rm{\blue{\longrightarrow \: \: Distance \: = \: Speed \: \times \: Time}}}$

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★ Question :-

A man travels from Cuttack to Bhubaneshwar at the speed of 50 km per hour and reaches in 30 minutes. Then he travels from Bhubaneshwar to Puri at the speed of 60 km per hour and reaches in 1 hour. What is his average speed ?

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★ Solution :-

Given,

» Speed in journey from Cuttack to Bhubaneswar = S = 50 Km/hr

» Speed in journey from Bhubaneswar to Puri = S' = 60 Km/hr

» Time taken in journey from Cuttack to Bhubaneswar = T = 30 mins = ½(30) hr = 0.5 hr

» Time taken in journey from Bhubaneswar to Puri = T' = 1 hour

Now let us calculate the things required.

~ Case I (for journey from Cuttack to Bhubaneswar) :-

Let the distance covered in this journey be D km.

➔ Distance = Speed × Time

➔ D = S × T

➔ D = 50 × 0.5

➔ D = 25 Km

~ Case II (for journey from Bhubaneswar to Puri) :-

Let the distance covered be D' Km.

➔ Distance = Speed × Time

➔ D' = S' × T'

➔ D = 60 × 1

➔ D = 60 Km

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From above results, we get,

• Total Distance covered by man = D + D'

= (60 + 25 ) Km = 85 Km

• Total time taken by the man to cover this distance = T + T' = (1 + 0.5) hr = 1.5 hr

Now let us apply these values, in our answer.

$\: \: \bf{\purple{\Longrightarrow \: \: Average \: Speed, \: (v_{av}) \: = \: \dfrac{Total \: Distance}{Total \: Time}}}$

$\: \: \huge{\bf{\orange{\Longrightarrow \: \: \: Average \: Speed, \: (v_{av}) \: = \: \dfrac{85 \: Km}{1.5 \: hr}}}}$

$\: \: \huge{\bf{\orange{\Longrightarrow \: \: Average \: Speed, \: (v_{av}) \: = \: 56.667 \: \: Kmhr^{-1}}}}$

$\\\\\\ \: \: \underline{\boxed{\sf{\red{\mapsto \: \: Hence, \: the \: average \: speed \: of \: the \: man \: is \: \underline{56.667 \: Kmhr^{-1}}}}}}$

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$\: \: \underline{\boxed{\rm{\pink{\mapsto \: \: Refer \: here \: for \: supplementary \: counsel}}}}$

• Speed is the distance covered in a unit time in any direction. Its a scalar quantity. Its unit is m/sec.

• Velocity is the distance covered in a init time in a certain direction. Its a vector quantity. Its unit is m/sec.

• Acceleration is the rate of change of velocity in a certain time. Its a vector quantity. Its unit is m/sec².

• Uniform Speed : an object is said to be moving with uniform speed if it covers equal distances in equal intervals of time, however small these time intervals may be.

• Variable Speed : an object is said to be moving with variable speed if it covers unequal distances in equal intervals of time, however small the distances be.