Question

A man travels with a speed 30 kmph for first half of the journey time and with a speed of 70 kmph for the next half of the journey time. Find the average speed of the man is
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Answer 1

Given :

A man travels with a speed 30 kmph for first half of the journey time and with a speed of 70 kmph for the next half of the journey time.

To find :

• Average speed of the man

Solution :

• In case : 1

A man travels with a speed 30 kmph for first half of the journey time

• Speed = 30 kmph
• Time (t1) = t/2 hour
• Distance (D1) = ?

As we know that

→ Speed = distance/time

→ Distance = Speed × time

According to the first question

→ D1 = 30 × ½

→ D1 = 15t km

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• In Case : 2

With a speed of 70 kmph for the next half of the journey time.

• Speed = 70kmph
• Time (t2) = t/2 hour
• Distance (D2) = ?

→ Distance = speed × time

→ D2 = 70 × t/2

→ D2 = 35t km

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★ Average speed ★

→ Total distance travelled/total time taken

→ D1 + D2/t1 + t2

→ 15t + 30t/t/2 + t/2

→ 50t/2t/2

→ 50t × 2/2t

→ 50 kmph

•°• Average speed of a man is 50kmph

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Answer 2

Answer:

Given :-

• A man travels with a speed of 30 kmph for first half of the journey time and with a speed of 70 kmph for the next half of the journey time.

To Find :-

• What is the average speed of the man.

Formula Used :-

To find distance we know that,

✯ Distance = Speed × Time ✯

To find average speed we know that,

★ Average Speed = Total distance travelled/Total time taken ★

Solution :-

In first case :-

Given :

• Speed (s₁) = 30 kmph
• Time (t₁) = ½ hour

According to the question by using the formula we get,

⇒ Distance (d₁) = 30 × ½

➠ Distance (d₁) = 15 km

In second case :-

Given :

• Speed (s₂) = 70 kmph
• Time (t₂) = ½ hour

According to the question by using the formula we get,

↦ Distance (d₂) = 70 = ½

➦ Distance (d₂) = 35 km

Now, we have to find the average speed of the man,

Given :

• d₁ = 15 km
• d₂ = 35 km
• t₁ = ½
• t₂ = ½

According to the question by using the formula we get,

⇒ Average Speed = 15 + 35/½ + ½

⇒ Average Speed = 50/2/2

⇒ Average Speed = 50 × 2/2

⇒ Average Speed = 50 × 1

➦ Average Speed = 50 kmph.

∴ The average speed of the man is 50 kmph .